Professor and Queen's Research ChairE-mail:murty at mast dot queensu dot ca |

Office: Jeffery Hall, Room 315Office Hours: By appointmentOffice Phone: (613) 533-2413Office FAX: (613) 533-2964 |
Department of Mathematics, Jeffery Hall, 99 University Avenue, Queen's University, Kingston, Ontario, K7L 3N6, Canada |

Assignment 1

Assignment 2

Sample midterm test questions

Midterm test Solutions to the Midterm test

Assignment 3

Assignment 1

Assignment 2 Central Limit Theorem via Fourier transforms

Assignment 3

Final Exam

Panorama Lectures: Ramanujan Conjectures and Zeta Functions |
Problems in the Theory of Modular Forms |
Transcendental Numbers |
Indian Philosophy: An Introduction |
The Mathematical Legacy of Srinivasa Ramanujan |
A First Course in Graph Theory and Combinatorics |
Automorphic L-functions |

Ramanujan Mathematical Society, 2018 |
(with M. Dewar & H. Graves), IMSc Lecture Notes, 2015 |
(with P. Rath), Springer, 2014. |
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. |

Problems in Analytic Number Theory |
Intro. to sieve methods and their applications |
Problems in Algebraic Number Theory, 2nd Ed. |
Introduction to p-adic analytic number theory, |
Non-vanishing of L-functions and applications |

Springer, 2nd edition, 2008 | (with A. Cojocaru)
Cambridge Univ. Press, 2006 |
(with J. Esmonde), Springer 2005 |
International Press, 2002 | (with V. Kumar Murty) Balaguer Prize Book Birkhauser, 1997 |

More research description can be found at CICMA

- 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.
- Simons Fellowship, 2013-2014.

- Ian Miyamoto, Primes and elliptic curves, M.Sc. thesis, McGill University, 1988.
- David Clark, L-series and ranks of elliptic curves, M.Sc. thesis, McGill University, 1988. (clark@math.byu.edu)
- David Clark, The Euclidean algorithm for Galois extensions of the rational numbers, Ph.D. thesis, McGill University, 1992.(clark@math.byu.edu)
- Tomasz Stefanicki, Non-vanishing of L-functions attached to automorphic representations of GL(2), Ph.D. thesis, McGill University, 1992.
- Francesco Pappalardi, On Artin's conjecture for primitive roots, Ph.D. thesis, McGill University, 1993. (pappa@mat.uniroma3.it)
- Chantal David, Supersingular Drinfeld modules, Ph.D. thesis, McGill University, 1993. (chantal@discrete.concordia.ca)
- Ashwaq Hashim, Application of Lindelof hypothesis to cusp forms, M.Sc. thesis, McGill University, 1993. (ucakash@ucl.ac.uk)
- Yuanli Zhang, Some analytic properties of automorphic L-functions, Ph.D. thesis, McGill University, 1994.(yz@math.purdue.edu)
- Sridhar Narayanan, Selberg's conjectures, M.Sc. thesis, McGill University, 1994.(sri@esankya.com)
- Keldon Drudge, The ABC Conjecture, M.Sc. Thesis, McGill University, 1995.
- Minatsu Yamaji, Applications of Brauer Induction to Artin L-functions, M.Sc. Thesis, McGill University, 1996.
- Francesco Sica, The order of vanishing of L-functions at the center of the critical strip, Ph.D. thesis, McGill University, 1998.
- Satya Mohit, The Wieferich criterion, the ABC conjecture and Shimura's correspondence, M.Sc. thesis, Queen's University, 1998.
- Yu-Ru Liu, The Turan sieve and some of its applications, M.Sc. thesis, Queen's University, 1998.(yrliu@math.harvard.edu)
- Filip Saidak, On conjectures about the distribution of primes in various sequences, M.Sc. thesis, Queen's University, 1998.(filips@math.ucalgary.ca)
- Malcolm Harper (PhD, McGill), A proof that $Z[\sqrt{14}]$ is Euclidean, Ph.D. thesis, McGill University, 2000.
- Steven Pope, On Problems of Cryptography: Primality testing and Factoring integers, M.Sc. thesis, Queen's University, 2000.
- Filip Saidak, On non-abelian generalizatons of the Erdös-Kac theorem, Ph.D. thesis, Queen's University, 2001.
- Alina Cojocaru, Cyclicity of Elliptic Curves modulo p, Ph.D. thesis, Queen's University, 2002.
- Kaneenika Sinha, Generalized Hurwitz zeta functions, (MSc, Queen's, 2002).
- Talia Borodin, Primality Testing and Factoring, (M.Sc., Queen's, 2003).
- Benjamin Ju, Elementary Proofs of the Prime Number Theorem, (M.Sc., Queen's, 2003).
- Tim Wotherspoon, Analysis of the Narayana-Fermat Factoring Algorithm(M.Sc., Queens, 2004).
- Jeanine Van Order, Counting Integral Ideals in an Algebraic Number Field,(M.Sc., Queen's, 2005).
- Sebastian Cioaba, Eigenvalues, Expanders and Gaps between Primes, (Ph.D., Queen's, 2005).
- Kaneenika Sinha, Effective Equidistribution of Eigenvalues of Hecke Operators, (Ph.D., Queen's, 2006).
- Brandon Fodden, Diophantine equations and the Generalized Riemann hypothesis (Ph.D., Queen's, 2007).
- Marilyn Reece Myers, Variations of Kummer's Conjecture (Ph.D., Queen's, 2007).
- Chester Weatherby, Transcendence of various infinite series and applications of Baker's theorem (Ph.D., Queen's, 2009).
- Robert Rundle, Generalized Pythagorean Triples (M.Sc., Queen's, 2007).
- Adam Felix, The order of a mod p and Artin's conjecture(M.Sc., Queen's, 2007).
- Andrew Droll, Properties of Ramanujan graphs (M.Sc., Queen's, 2008).
- Marc Papais, Graph spectra and the Ihara zeta function: implications and connections (M.Sc., Queen's, 2008).
- Carpio Cheng, Grimm's conjecture and a Gaussian analogue, (M.Sc. Queen's, 2009).
- Adam Felix,, Variations on Artin's primitive root conjecture (Ph.D., Queen's, 2011)
- Robert Rundle, Generalization of Ruderman's problem to imaginary quadratic fields (Ph.D., Queen's, 2012)
- Andrew Droll,, Variations of Li's criterion for an extension of the Selberg class (Ph.D., Queen's, 2012).
- Ryan Case, Ramanujan-Fourier series and applications (M.Sc., Queen's, 2013).
- Hector Pasten, Arithmetic problems around the abc conjecture and connections with logic, (Ph.D., Queen's, 2014).
- Siddhi Pathak, The Chowla problem and its generalizations, (M.Sc., Queen's, 2015)
- Kannappan Sampath , The saddle point method and its applications to number theory(M.Sc., Queen's, 2015)
- Akshaa Vatwani, Higher rank sieves and applications(Ph.D., Queen's, 2016).
- Arpita Kar, Representation of numbers by quaternary quadratic forms, (M.Sc. Queen's, 2016).
- Peng-Jie Wong, Character theory and Artin L-functions (Ph.D., Queen's, 2017).
- Francois Seguin, The two-variable Artin conjecture and elliptic analogues (Ph.D., Queen's, 2018)
- Siddhi Pathak,(Ph.D., Queen's, in progress).
- Arpita Kar, (Ph.D., Queen's, in progress).