Ram Murty - Publications by Year

The dvi files below are given for the benefit of those who may not have access to the respective journal. They may not contain changes made in the final proofs.
  1. Irrational numbers arising from certain differential equations, (with V. Kumar Murty), Canadian Math. Bulletin, 20 (1977) 117-120.

    1979

  2. Some results in number theory I, (with V. Kumar Murty), Acta Arithmetica, 35 (1979) 367-371.

    1980

  3. On the Redei zeta function, (with J.P. Kung and G.-C. Rota), Journal of Number Theory,12 (1980) 421-436.

    1982

  4. An Omega theorem for Ramanujan's tau function, (with R. Balasubramanian), Inventiones Mathematicae, 68 (1982) 241-252.
  5. Some Omega results for Ramanujan's tau function, Proceedings of the Number Theory Conference at Mysore, Springer Lecture Notes, 938 (1982) 123-137.

    1983

  6. On the density of various classes of groups, (with V. Kumar Murty), Journal of Number Theory, 17 (1983) 29-36.
  7. On Artin's conjecture, Journal of Number Theory, 16 (1983) 147-168.
  8. Oscillations of Fourier coefficients of modular forms, Math. Annalen, 262 (1983) 431-446.

    1984

  9. An analogue of Artin's conjecture for abelian extensions, Journal of Number Theory, 18 (1984) 241-248.
  10. A remark on Artin's conjecture, (with R. Gupta), Inventiones Mathematicae, 78 (1984) 127-130.
  11. Prime divisors of Fourier coefficients of modular forms, (with V. Kumar Murty), Duke Math. Journal, 51 (1984) 57-77.
  12. On groups of squarefree order, (with V. Kumar Murty), Math. Annalen, 267 (1984) 299-309.
  13. On the number of groups of a given order, (with V. Kumar Murty), Journal of Number Theory, 18 (1984) 178-191.
  14. An analogue of the Erdös-Kac theorem for Fourier coefficients of modular forms, (with V. Kumar Murty), Indian Journal of Pure and Applied Mathematics, 15 (1984) 1090-1101.

    1985

  15. On the estimation of eigenvalues of Hecke operators, Rocky Mountain Journal of Mathematics, 15 (2) (1985) 521-533.

    1986

  16. Primitive points on elliptic curves, (with R. Gupta), Compositio Math., 58 (1986) 13-44.

    1987

  17. On the enumeration of finite groups, (with P. Erdös and V. Kumar Murty), Journal of Number Theory 25 (1987) 360-378.
  18. Some remarks on Artin's conjecture, (with S. Srinivasan), Canadian Math. Bulletin, 30 (1987) 80-85.
  19. Odd values of the Ramanujan tau function, (with V. Kumar Murty and T. N. Shorey), Bulletin Soc. Math. France, 115 (1987) 391-395.
  20. On the number of groups of squarefree order, (with S. Srinivasan), Canadian Math. Bulletin, 30 (4) (1987) 412-420.
  21. On the sieve of Eratosthenes, (with N. Saradha), Canadian Journal of Mathematics, 39 (5) (1987) 1107-1122.
  22. On the supersingular reduction of elliptic curves, Proceedings of the Indian Academy of Sciences, 97 (1-3) (1987) 247-250.
  23. A variant of the Bombieri-Vinogradov theorem, (with V. Kumar Murty), Number Theory, Proceedings of the 1985 Montreal conference, 7 (1987) 243-272.
  24. The Euclidean algorithm for S integers, (with R. Gupta and V. Kumar Murty), Number Theory, Proceedings of the 1985 Montreal conference (ed. H. Kisilevsky and J. Labute), 7 (1987) 189-201.
  25. On Ramanujan's tau function, Ramanujan Revisited, Proceedings of the Illinois conference on Ramanujan, (1987) 269-288.
  26. An introduction to Selberg's trace formula, Journal of Indian Math. Society, 52 (1987) 91-126.

    1988

  27. Modular forms and the Chebotarev density theorem, (with V. Kumar Murty and N. Saradha), American Journal of Mathematics, 110 (1988) 253-281
  28. Primes in certain arithmetic progressions, Journal of the Madras University, (1988) 161-169.
  29. Recent developments in elliptic curves, Proceedings of the Ramanujan Centennial International Conference, 1 (1988) 45-53.
  30. Prime numbers, explicit formulas and the Riemann hypothesis, Quebec Math. Gazette, 12 (3) (1988) 3-15.
  31. Artin's conjecture for primitive roots, Math. Intelligencer, 10 (4) (1988) 59-67.

    1989

  32. Elliptic pseudoprimes, (with I. Miyamoto), Mathematics of Computation, 53 (187) (1989) 415-430.
  33. Elliptic pseudoprimes, II, (with R. Balasubramanian), Seminaire de Theorie des Nombres, Paris 1988-89, (1989) 13-25, Birkhauser-Verlag.
  34. L-series of automorphic forms on GL_3(R), (with Jeff Hoffstein), Number Theory, (J.-M. de Koninck and C. Levesque, eds.) (1989) 398-408, Walter de Gruyter.
  35. Review of An introduction to the theory of the Riemann zeta function, by S.J. Patterson, Cambridge Studies in Advanced Mathematics, Volume 14, Cambridge University Press, Cambridge and New York, (1988) 156 pages and of Introduction to analytic number theory, by A. G. Postnikov, Translations of Mathematical Monographs, Volume 68, American Mathematical Society, Providence, R.I., (1988) 320 pages in Bulletin of the American Mathematical Society, 20 (1989) 226-229.

    1990

  36. Cyclicity and generation of points mod p on elliptic curves, (with Rajiv Gupta), Inventiones Math., 101 (1990) 225-235.
  37. On simple zeroes of certain L-series, Number Theory (R. Mollin, ed.), (1990) 427-439, (Walter de Gruyter).
  38. Automorphic forms and analytic number theory (Editor), CRM, 1990.

    1991

  39. Mean values of derivatives of modular L-series, (with V. Kumar Murty), Annals of Mathematics, 133 (1991) 447-475.
  40. Elliptic curves and modular forms, Canadian Math. Bulletin, 34 (3) (1991) 375-384.

    1992

  41. Le programme de Langlands, Quebec Math. Gazette, 14 (2) (1992) 20-26.
  42. Theta functions, CRM, 1992.

    1993

  43. Base change and the Birch-Swinnerton-Dyer conjecture, Contemporary Mathematics, 143 (1993) 481-494, American Mathematical Society.
  44. An asymptotic formula by a method of Selberg, (with N. Saradha), Comptes Rendus Acad. Sci. (Canada), 15 (6) (1993) 273-277.
  45. Appendix to a paper of R.A. Smith, C.R.Math. Rep. Acad. Sci. Canada 15(1993) p. 91-98.
  46. A motivated introduction to the Langlands program, in Advances in Number Theory, (eds. F. Gouvêa and N. Yui), (1993) 37-66, Clarendon Press, Oxford.
  47. Theta functions: from the classical to the modern, CRM Proceedings and Lecture Notes, I, (editor).
  48. Topics in Number Theory, MRI Lecture Notes, 1993.

    1994

  49. On Zagier's cusp form and the Ramanujan tau function, (with Ashwaq Hashim), Proceedings of the Indian Academy of Sciences, 104 (1) (1994) 93-98.
  50. Selberg conjectures and Artin L-functions, Bulletin of the American Mathematical Society, 31 (1) (1994) 1-14.
  51. Finitely generated groups (mod p), Proceedings of the American Mathematical Society, 122 (1) (1994) 37-45.
  52. Strong multiplicity one for Selberg's class, (with V. Kumar Murty), Comptes Rendus Acad. Sci. Paris, 319 Series I (1994) 315-320.
  53. The Phragmen-Lindelof theorem and modular elliptic curves, (with Liem Mai), H. Rademacher Centenary Volume, Contemporary Math., 166 (1994) 335-340, Amer. Math. Society, Providence.
  54. A note on the quadratic twists of an elliptic curve, (with Liem Mai), Proceedings of the Ste. Adele Conference, (eds. H. Kisilevsky and R. Murty), CRM (1994) 121-124, American Math. Society, Providence.
  55. Elliptic curves and related objects, (Co-editor with H. Kisilevsky), CRM Proceedings and Lecture Notes, 4, 1994.

    1995

  56. The Euclidean algorithm in Galois extensions of Q, (with David Clark), Journal fur die reine und angewandte Mathematik, 459 (1995) 151-162.
  57. Supersingular primes common to two elliptic curves, (with E. Fouvry), London Mathematical Society Lecture Notes Series 215, Number Theory, Paris 1992-93, (ed. Sinnou David), (1995) 91-102, Cambridge University Press.
  58. Selberg's conjectures and Artin L-functions, II, in Current Trends in Mathematics and Physics, A tribute to Harish-Chandra, edited by S. D. Adhikari, Narosa Publishing House, 1995.
  59. On the rank of J0(N)(Q), in the Halifax Proceedings in Number Theory (ed. K. Dilcher), Canadian Mathematical Society 15 (1995) 263-277.
  60. Reflections on Fermat's Last Theorem, Elemente der Mathematik 50 (1995) 3-11.

    1996

  61. On the distribution of supersingular primes, (with Étienne Fouvry), Canadian Journal of Math. 48 (1) (1996) 81-104.
  62. A variation on a theme of Romanoff, (with M. Rosen and J. Silverman), International Journal of Mathematics, Vol. 7, No. 3 (1996) 373-391.
  63. Counting finite groups, in Analysis, Geometry and Probability, edited by Rajendra Bhatia, Hindustan Book Agency, (1996) 161-172.
  64. Stronger multiplicity one theorems for forms of general type on GL(2), (with C.S. Rajan), in Analytic Number Theory, Proceedings of the Number Theory Conference in honour of H. Halberstam, (eds. B. Berndt, H. Diamond, and A. Hildebrand), Progress in Mathematics, Vol. 139, (1996), 669-683, Birkhauser.
  65. Artin's conjecture and elliptic analogues, in Sieve Methods, Exponential Sums, and their Applications in Number Theory, (eds. G.R.H. Greaves, G. Harman, and M.N. Huxley) (1996) 325-344, Cambridge University Press.

    1997

  66. Congruences between modular forms, in Analytic Number Theory, (ed. Y. Motohashi), London Mathematical Society Lecture Notes 247 (1997) 313-320, Cambridge University Press.
  67. The ABC Conjecture and Exponents of Class Groups of Quadratic Fields, in Number Theory (edited by V. Kumar Murty and Michel Waldschmidt), Contemporary Math. 210, AMS, 1997, p. 85-95.
  68. Stronger multiplicity one for Selberg's Class, in Harmonic Analysis and Number Theory (Papers in honour of Carl Herz) (eds. S. Drury and R. Murty), Canadian Math. Society Conf. Proceedings, (1997) Vol. 21, pp. 133-142.
  69. Non-vanishing of L-functions, in Advances in Mathematical Sciences: CRM's 25 Years, (edited by Luc Vinet), CRM Proceedings and Lecture Notes, Volume 11, 1997, p. 319-328.
  70. Non-vanishing of L-functions and applications, (with V. Kumar Murty), Progress in Mathematics, 157, (Ferran Sunyer i Balauger Award Winning Monograph), Birkhauser, 1997.
  71. Harmonic analysis and number theory, (co-editor with S. Drury), CMS Conference Proceedings, Vol. 21, Amer. Math. Soc. 1997.

    1998

  72. Artin's conjecture for polynomials over finite fields, (with Erik Jensen), in Number Theory (edited by R.P. Bambah, V. Dumir and R.J. Hans Gill), Birkhauser-Verlag, 2000, pp. 167-181.
  73. Wieferich primes and Hall's conjecture, (with Satya Mohit), Comptes Rendus de l'Acad. Science (Canada), Vol. 20, No. 1, (1998) 29-32.
  74. Bounds for congruence primes, in Automorphic Forms, Automorphic Representations and Arithmetic, edited by R. Doran, Ze-Li Dou and G. Gilbert, Proceedings of Symposia in Pure Mathematics, Vol. 66, Part 1, pp. 177-192, Amer. Math. Soc., 1999.
  75. Problems in Algebraic Number Theory, (with Jody Esmonde), Graduate Texts in Mathematics, 190, Springer-Verlag, 1998.

    1999

  76. Exponents of class groups of quadratic fields, in Topics in Number Theory, (edited by S. Ahlgren, G. Andrews and K. Ono), pp. 229-239, 1999, Kluwer, Netherlands.
  77. On the order of a mod p, (with P. Erdös), CRM Proceedings and Lecture Notes, Volume 19, (1999) pp. 87-97.
  78. The Turan sieve method and some of its applications, (with Yu-ru Liu), Journal of the Ramanujan Mathematical Society, Vol. 13, No. 2, (1999) pp. 35-49.
  79. The pair correlation of zeros of functions in the Selberg class, (with A. Perelli), International Math. Res. Notices. (1999) Vol. 10, p. 531-545.

    2000

  80. The work of Sarvadaman Chowla (with V. Kumar Murty and K.S. Williams), in the Collected Papers of Sarvadaman Chowla, CRM, 2000.
  81. Variations on a conjecture of Dedekind (with A. Raghuram), Journal of the Ramanujan Math. Society, 15, No. 2, (2000) pp. 75-95.
  82. Review of `Elementary Methods in Number Theory,' Bulletin of the Amer. Math. Soc., 2000, Vol. 38, Number 1, pp. 117-121.
  83. A simple derivation of $\zeta(1-k)=-B_k/k$, (with Marilyn Reece), Functiones et Approximatio, XXVIII (2000) 141-154.

    2001

  84. Some Remarks on the Riemann Hypothesis, in ``Cohomology of Arithmetic Groups, L-Functions and Automorphic Forms, (edited by T. N. Venkataramana), TIFR, Narosa Publishing House, pp. 180-196, Mumbai, India.
  85. Problems in Analytic Number Theory, GTM/RIM Vol. 206, Springer-Verlag, 2001.
  86. On Kummer's conjecture, (with Yiannis Petridis),Journal of Number Theory, Vol. 90, 2001, pp. 294-303.
  87. An Introduction to Artin L-functions, Journal of the Ramanujan Mathematical Society, Vol. 16, No. 3, 2001, pp. 261-307.
  88. Artin L-functions, in Class Field Theory - its centenary and prospect, (Tokyo, 1998), pp. 13-29, Advanced Studies in Pure Math., Vol. 30, Math. Soc. Japan, Tokyo, 2001.
  89. Exponents of class groups of quadratic function fields over finite fields, (with David Cardon), Canadian Math. Bulletin., Vol. 44 (4), 2001, pp. 398-407.
  90. Quadratic reciprocity via linear algebra, Bona Mathematica, Vol. 12, No. 4, (2001), 75-80.

    2002

  91. On the distinctness of decimations of l-sequences, (with M. Goresky, A. Klapper) in T. Helleseth, ed. Sequences and their applications, Proceedings of SETA '01, Discrete Mathematics and Computer Science, Springer-Verlag, New York, 2002.
  92. Explicit formulas for the pair correlation of zeros of functions in the Selberg class (with A. Zaharescu), Forum Math., Vol. 14, 2002, no. 1, 65-83.
  93. Averages of Exponential Twists of the Liouville function (with A. Sankaranarayanan), Forum Math., Vol. 14, 2002, no. 2, 273-291.
  94. Prime Numbers and Irreducible Polynomials, Amer. Math. Monthly, Vol. 109 (2002), no. 5, 452-458.
  95. Introduction to $p$-adic analytic number theory, AMS/IP Studies in Advanced Mathematics, 27, American Math. Society, Providence, RI, International Press, 2002, 149pp.
  96. Recent developments in the Langlands program, C. R. Math. Acad. Sci. Soc. R. Can. 24 (2002), no. 2, 33-54.
  97. Sieving using Dirichlet series,in Current Trends in Number Theory, edited by S. Adhikari, S.A. Katre, and B. Ramakrishnan, Hindustan Book Agency, 2002, pp. 111-124.
  98. The ABC conjecture and prime divisors of the Lucas and Lehmer sequences, (with Siman Wong), in Number Theory for the Millenium, Vol. 3, (edited by M. Bennett et al), 2002, pp. 43-54, A.K. Peters.

    2003

  99. On the number of real quadratic fields with class number divisible by 3,(with K. Chakraborty) Proceedings of the Amer. Math. Soc., 131(2003), no. 1, 41-44.
  100. Irreducibility of Hecke polynomials, (with Srinath Baba), Math. Research Letters, 10(2003), no. 5-6, 709-715.
  101. Ramanujan Graphs, Journal of the Ramanujan Math. Society, 18, No. 1, (2003), 1-20.
  102. Sieve methods, Siegel zeros and Sarvadaman Chowla, in Connected at Infinity, Texts and Readings in Mathematics, Hindustan Book Agency, 2003, pp. 18-35.

    2004

  103. Non-abelian generalizations of the Erdos-Kac theorem, (with F. Saidak), Canadian Journal of Math., Vol. 56 (2004), no. 2, 356-372.
  104. On decimations of l-sequences, (with M. Goresky, A. Klapper, and I. Shparlinski), SIAM J. Discrete Math., Vol. 18 (2004), no. 1, p. 130-140.
  105. Euclidean rings of Algebraic Integers, (with M. Harper) Canadian Journal of Math., Vo.. 56 (2004), no. 1, p. 71-76.
  106. Lectures on Automorphic L-functions, (with James Cogdell and Henry Kim), Fields Institute Monograph Series, Volume 20, 2004, 283p.
  107. Pair Correlation Conjecture and the Chebotarev Density Theorem (with V. Kumar Murty), preprint.
  108. Summatory functions of elements in the Selberg class, (with Wentang Kuo), Algebraic Groups and arithmetic, Tata Institute of Fundamental Research, 2004, pp. 525-538.
  109. An application of Mumford's gap principle, (with Jung-Jo Lee), Journal of Number Theory, 105 (2004), no. 2, 333-343.
  110. Cyclicity of elliptic curves modulo p and elliptic curve analogues of Linnik's problem, (with A. Cojocaru), Math. Annalen, 330 (2004), no. 3, 601-625.

    2005

  111. On a conjecture of Birch and Swinnerton-Dyer, (with Wentang Kuo), Canadian Journal of Math., 57 (2005), no. 2, 328-337.
  112. Problems in Algebraic Number Theory (with J. Esmonde), Second Edition, Graduate Texts in Mathematics, 190, Springer-Verlag, 2005.
  113. Sieve methods in combinatorics, (with Yu-Ru Liu), Journal of Combinatorial Theory, Series A., 111 (2005), no. 1, 1-23.
  114. Quadratic reciprocity via theta functions, (with Allison Pacelli), Ramanujan Math. Society Lecture Notes, Volume 1, (2005), pp. 107-116.
  115. The square sieve and the Lang-Trotter conjecture, (with A. Cojocaru and E. Fouvry), Canadian Journal of Math., 57 (2005), no. 6, 1155-1177.

    2006

  116. The weighted Turan sieve,(with Yu-Ru Liu), Journal of Number Theory, 116 (2006), no. 1, 1-20.
  117. Spectral Estimates for Abelian Cayley Graphs, (with J. Friedman and J.-P. Tillich), J. Combin. Theory Ser. B. 96 (2006), no. 1, 111-121.
  118. Multiple Hurwitz zeta functions, (with K. Sinha), in Multiple Dirichlet series, automorphic forms, and analytic number theory, Proc. Symp. Pure Math., 75 (2006), 135-156.
  119. Applications of Sieve Methods, (with A. Cojocaru), Cambridge University Press, London Mathematical Society Student Texts, 66 (2006), 224p.
  120. Irreducible polynomials over number fields, (with Jasbir Chahal), in The Riemann zeta function and related themes: papers in honour of Professor K. Ramachandra, Ramanujan Math. Soc. Lecture Notes Ser., 2 (2006), 39-43.
  121. Prime numbers in certain arithmetic progressions, (with N. Thain), Funct. Approx. Comm. Math., 35 (2006), 249-259.

    2007

  122. Pick's theorem via Minkowski's theorem, (with N. Thain), American Math. Monthly, 114 (2007), 732-736.
  123. Transcendental values of the digamma function, (with N. Saradha), Journal of Number Theory, 125 (2007), no. 2, 298-318.
  124. Dirichlet series and hyperelliptic curves (with Jung-Jo Lee), Forum Math., 19 (2007), no. 4, 677-705.
  125. Sudoku squares and chromatic polynomials, (with A. Herzberg), Notices of the Amer. Math. Soc., 54 (2007) no. 6, 708-717.
  126. Counting integral ideals in a number field, (with J. Van Order), Expo. Math., 25 (2007), no. 1, 53-66.
  127. Odd values of Fourier coefficients of certain modular forms, (with V. Kumar Murty), International Journal of Number Theory, 3 (2007), 455-470.
  128. Group structure of elliptic curves over finite fields and applications, in Topics in geometry, coding theory and cryptography, Algebr. Appl., 6, Springer, Dordrecht, 2007, 167-198.
  129. Representations of integers by certain positive definite binary quadratic forms, (with R. Osburn), 14 (2007) no. 3, 351-359.

    2008

  130. On a conjecture of Shorey, (with V. Kumar Murty), Diophantine equations, Tata Institute for Fundamental Research Studies, Volume 20, 2008, 167-176.
  131. Uniform distribution of zeros of Dirichlet series, (with A. Akbary), CRM Conference Proceedings: Anatomy of Integers, Lecture Notes Ser., Volume 46, 2008, pp. 143-158.
  132. Summation methods and distribution of eigenvalues of Hecke operators, (with S. Gun and P. Rath), Funct. Approx. Comment. Math., 39 (2008), part 2, 191-204.
  133. On a generalisation of Artin's conjecture, (with C. Franc), Pure and Applied Math. Quarterly, 4 (2008), no. 4, 349-362.
  134. Transcendental numbers and zeta functions, Math. Student, 77 (2008), no. 1-4, 87-101.
  135. Polynomials assuming square values,, Number Theory and Discrete Geometry, Ramanujan Math. Society Lecture Notes Ser., 6, 155-163, 2008.

    2009

  136. Special values of the polygamma functions, (with N. Saradha), International Journal of Number Theory 5(2009), no. 3, 681-714.
  137. Effective equidistribution of eigenvalues of Hecke operators, (with K. Sinha), J. Number Theory, 129 (2009), no. 3, 681-714.
  138. Linear independence of the digamma function and a variant of a conjecture of Rohrlich, (with S. Gun and P. Rath), Journal of Number Theory, 129 (2009), no. 8, 1858-1873.
  139. Countine squarefree discriminants of trinomials under abc, (with A. Mukhopadhyay and K. Srinivas), Proc. Amer. Math. Soc., 137 (2009), no. 10, 3219-3226.
  140. Transcendence of the log gamma functin and some discrete periods, (with S. Gun and P. Rath), Journal of Number Theory, 129 (2009), no. 9, 2154-2165.
  141. The generalized Artin conjecture and arithmetic orbifolds, (with K. Petersen), CRM Conference Proceedings, Volume 47 (2009), 259-265.
  142. A first course in graph theory and combinatorics, (with S. Cioaba), Hindustan Book Agency, 55, 2009, New Delhi. Errata
  143. Variations of Sato-Tate Conjecture, Number Theory and applications, Hindustan Book Agency, New Delhi, 2009, 127-138.

    2010

  144. Small solutions of polynomial congruences, Indian J. Pure Appl. Math., 41 (2010), no. 1, 15-23.
  145. Factoring newparts of Jacobians of certain modular curves, (with K. Sinha), Proceedings of the Amer. Math. Society, 138 (2010), no. 10, 3481-3494.

    2011

  146. Effective equidistribution and the Sato-Tate law for families of elliptic curves, (with Steven J. Miller), Journal of Number theory, 131 (2011)25-44.
  147. A problem of Chowla revisited, (with V. Kumar Murty), Journal of Number Theory, 131 (2011), 1723-1733.
  148. On a conjecture of Chowla and Milnor (with S. Gun and P. Rath), Canadian Journal of Mathematics, 2011.
  149. Transcendental nature of special values of L-functions, (with S. Gun and P. Rath), Canadian Journal of Mathematics, 2011.
  150. A variant of the Lang-Trotter conjecture, (with V. Kumar Murty), to appear.
  151. Primitive roots along curves and varieties (with K. Guruprasad), in preparation.
  152. Class groups of quadratic function fields, (with R. Gupta), in preparation.