# Ram Murty

 Professor and Queen's Research Chair E-mail:murty at mast dot queensu dot ca

 Office: Jeffery Hall, Room 312 Office Hours: By appointment Office Phone: (613) 533-2413 Office FAX: (613) 533-2964 Department of Mathematics, Jeffery Hall, 99 University Avenue, Queen's University, Kingston, Ontario, K7L 3N6, Canada

## Recent Books

 Indian Philosophy: An Introduction, The Mathematical Legacy of Srinivasa Ramanujan, A First Course in Graph Theory and Combinatorics, Automorphic L-functions Problems in Analytic Number Theory, Broadview Press, 2013. (with V. Kumar Murty), Springer, 2012. errata (with S. Cioaba), HBA, 2009 errata (with J. Cogdell and H. Kim), Fields Inst./AMS, 2009. Springer, 2nd edition, 2008

## Earlier Books

 Intro. to sieve methods and their applications Problems in AlgebraicNumber Theory, 2nd Ed. Introduction to p-adic analytic number theory, Non-vanishing of L-functions and applications (with A. Cojocaru) Cambridge Univ. Press, 2006 (with J. Esmonde), Springer 2005 International Press, 2002 (with V. Kumar Murty) Balaguer Prize BookBirkhauser, 1997

• Mathematics Colloquium
• Number Theory Seminar
• Number Theory at Queen's
• Mathscinet Search
• Number Theory Web
• Kumar Murty's Page
• Library/Queen's University
• JSTOR(Mathematics)

## Research Interests

Number Theory: Artin's conjecture, Elliptic curves, Modular Forms, Automorphic forms, Langlands Program, Selberg's conjectures, Sieve Methods, Cryptography
More research description can be found at CICMA
• Here is chronological list of publications: LIST
• This is the link for Mathematical Reviews of my papers.

## Degrees and Honours

• Ph.D. (MIT, 1980) (Advisor: Harold Stark)
• Coxeter-James Prize, 1988
• Fellow of the Royal Society of Canada (1990 - )
• E.W.R. Steacie Fellow (1991-1993)
• J.H.H. Nesbitt Lecturer, 1992
• Kenneth Ireland Lecturer, 1993
• Balaguer Prize (1996) jointly with V. Kumar Murty (see August 1996 issue of the Notices of the AMS)
• Killam Research Fellow (1998-2000)
• Jeffery-Williams Prize, 2003
• Queen's Research Chair, 2002
• Fellow of the Fields Institute, 2003
• Queen's Research Prize, 2003
• Adjunct Professor, McGill University (Montreal), Harish-Chandra Research Institute (Allahabad), Institute for Mathematical Sciences (Chennai), Chennai Mathematical Institute (Chennai), Indian Institute of Technology (Mumbai), Tata Institute for Fundamental Research (TIFR, Mumbai).
• Cross-appointment to the Department of Philosophy
• Elected fellow of the National Academy of Sciences (India), 2007.
• Elected fellow of the Indian National Science Academy (INSA), 2008.
• Elected fellow of the American Mathematical Society, 2012.

## Expository Lectures

• The Art of Research, 2005 Herzberg Lecture, Carleton University/Tata Institute for Fundamental Research, Mumbai, India.
• Ellipses and elliptic curves, Coleman-Ellis Lecture, March 30, 2006.
• Recent Developments in the Langlands Program, C.R. Math. Acad. Sci. R. Can., 24(2002), no. 2, 33-54.
• A Motivated Introduction to the Langlands Program, in Advances in Number Theory, (edited by F. Gouvea and N. Yui), pp. 37-66, Clarendon Press, Oxford, 1993.
• Ramanujan graphs, Journal of the Ramanujan Math. Society, 18, No. 1, (2003), 1-20.
• Selberg's conjectures and Artin L-functions, Bulletin of the American Math. Society, 31(1) (1994), 1-14.

## Recent Publications

• Sudoku squares and chromatic polynomials(with A. Herzberg), Notices of the Amer. Math. Society, 54(2007), no. 6, 708-717.
• 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.
• An introduction to sieve methods and their applications, (with A. Cojocaru) London Mathematical Society Student Texts, 66, Cambridge University Press, 2006.
• Problems in Analytic Number Theory, Graduate Texts in Mathematics, Vol. 206, Springer-Verlag, 2001.
• Lectures on Symmetric Power L-functions (Fields Institute, 2004)(pdf format)
• Problems in Algebraic Number Theory, (with J. Esmonde), Graduate Texts in Mathematics, 190, Springer-Verlag, 2005, 2nd edition.
• Non-vanishing of L-functions and Applications, Progress in Mathematics 157, Birkhauser, 1997 (Balaguer Prize Monograph), (with Vijaya Kumar Murty)
• Spectral Estimates for Abelian Cayley Graphs, (with J. Friedman and J-P. Tillich), Journal of Combinatorial Theory, Series B., 96(2006), no. 1, 111-121.
• The square sieve and the Lang-Trotter conjecture (with A. Cojocaru and E. Fouvry), Canadian Journal of Math., 57(6) (2005), 1155-1177.
• Sieve methods in combinatorics (with Y.-R. Liu), Journal of Combinatorial Theory, Series A, 111(2005), no. 1, 1-23.
• On decimations of l-sequences(with M. Goresky, A. Klapper, and I. Shparinski), SIAM Journal of Discrete Mathematics, 18 (2004), no. 1, 130-140.
• Euclidean rings of algebraic integers (with M. Harper), Canadian Journal of Mathematics, 56(2004), no. 1, 71-76.
• Cyclicity of elliptic curves modulo p and elliptic analogues of Linnik's problem, (with A. Cojocaru), Math. Annalen, 330 (2004), no. 3, 601-625.
• On a conjecture of Birch and Swinnerton-Dyer (with W. Kuo), Canadian Journal of Math., 57(2005), no. 2, 328-337.
• An application of Mumford's gap principle, (with J.J. Lee), Journal of Number Theory, 105(2004), no. 2, 333-343.

## Current Post-Doctoral Fellows:

Tapas Chatterjee, Alia Hamieh, Tom Hulse, Jaban Meher, Naomi Tanabe, Chester Weatherby.

## Theses supervised:

1. Ian Miyamoto, Primes and elliptic curves, M.Sc. thesis, McGill University, 1988.
2. David Clark, L-series and ranks of elliptic curves, M.Sc. thesis, McGill University, 1988. (clark@math.byu.edu)
3. David Clark, The Euclidean algorithm for Galois extensions of the rational numbers, Ph.D. thesis, McGill University, 1992.(clark@math.byu.edu)
4. Tomasz Stefanicki, Non-vanishing of L-functions attached to automorphic representations of GL(2), Ph.D. thesis, McGill University, 1992.
5. Francesco Pappalardi, On Artin's conjecture for primitive roots, Ph.D. thesis, McGill University, 1993. (pappa@mat.uniroma3.it)
6. Chantal David, Supersingular Drinfeld modules, Ph.D. thesis, McGill University, 1993. (chantal@discrete.concordia.ca)
7. Ashwaq Hashim, Application of Lindelof hypothesis to cusp forms, M.Sc. thesis, McGill University, 1993. (ucakash@ucl.ac.uk)
8. Yuanli Zhang, Some analytic properties of automorphic L-functions, Ph.D. thesis, McGill University, 1994.(yz@math.purdue.edu)
9. Sridhar Narayanan, Selberg's conjectures, M.Sc. thesis, McGill University, 1994.(sri@esankya.com)
10. Keldon Drudge, The ABC Conjecture, M.Sc. Thesis, McGill University, 1995.
11. Minatsu Yamaji, Applications of Brauer Induction to Artin L-functions, M.Sc. Thesis, McGill University, 1996.
12. Francesco Sica, The order of vanishing of L-functions at the center of the critical strip, Ph.D. thesis, McGill University, 1998.
13. Satya Mohit, The Wieferich criterion, the ABC conjecture and Shimura's correspondence, M.Sc. thesis, Queen's University, 1998.
14. Yu-Ru Liu, The Turan sieve and some of its applications, M.Sc. thesis, Queen's University, 1998.(yrliu@math.harvard.edu)
15. Filip Saidak, On conjectures about the distribution of primes in various sequences, M.Sc. thesis, Queen's University, 1998.(filips@math.ucalgary.ca)
16. Malcolm Harper (PhD, McGill), A proof that $Z[\sqrt{14}]$ is Euclidean, Ph.D. thesis, McGill University, 2000.
17. Steven Pope, On Problems of Cryptography: Primality testing and Factoring integers, M.Sc. thesis, Queen's University, 2000.
18. Filip Saidak, On non-abelian generalizatons of the Erdös-Kac theorem, Ph.D. thesis, Queen's University, 2001. (filips@math.ucalgary.c)
19. Alina Cojocaru, Cyclicity of Elliptic Curves modulo p, Ph.D. thesis, Queen's University, 2002 (alina@math.princeton.edu).
20. Kaneenika Sinha, Generalized Hurwitz zeta functions, (MSc, Queen's, 2002).
21. Talia Borodin, Primality Testing and Factoring, (M.Sc., Queen's, 2003).
22. Benjamin Ju, Elementary Proofs of the Prime Number Theorem, (M.Sc., Queen's, 2003).
23. Tim Wotherspoon, Analysis of the Narayana-Fermat Factoring Algorithm(M.Sc., Queens, 2004).
24. Jeanine Van Order, Counting Integral Ideals in an Algebraic Number Field,(M.Sc., Queen's, 2005).
25. Sebastian Cioaba, Eigenvalues, Expanders and Gaps between Primes, (Ph.D., Queen's, 2005).
26. Kaneenika Sinha, Effective Equidistribution of Eigenvalues of Hecke Operators, (Ph.D., Queen's, 2006).
27. Brandon Fodden, Diophantine equations and the Generalized Riemann hypothesis (Ph.D., Queen's, 2007).
28. Marilyn Reece Myers, Variations of Kummer's Conjecture (Ph.D., Queen's, 2007).
29. Chester Weatherby, Transcendence of various infinite series and applications of Baker's theorem (Ph.D., Queen's, 2009).
30. Robert Rundle, Generalized Pythagorean Triples (M.Sc., Queen's, 2007).
31. Adam Felix The order of a mod p and Artin's conjecture(M.Sc., Queen's, 2007).
32. Andrew Droll, Properties of Ramanujan graphs (M.Sc., Queen's, 2008).
33. Marc Papais, Graph spectra and the Ihara zeta function: implications and connections (M.Sc., Queen's, 2008).
34. Carpio Cheng, Grimm's conjecture and a Gaussian analogue, (M.Sc. Queen's, 2009).
35. Adam Felix, Variations on Artin's primitive root conjecture (Ph.D., Queen's, 2011)
36. Robert Rundle, Generalization of Ruderman's problem to imaginary quadratic fields (Ph.D., Queen's, 2012)
37. Andrew Droll, Variations of Li's criterion for an extension of the Selberg class (Ph.D., Queen's, 2012).
38. Hector Pasten, (Ph.D., Queen's, in progress).
39. Ryan Case, Ramanujan-Fourier series and applications (M.Sc., Queen's, in progress).
40. Akshaa Vatwani (Ph.D., Queen's, in progress).
41. Robert Embree (M.Sc., Queen's, in progress).
42. Pong-Jie Wong (Ph.D., Queen's, in progress).