Publications

1. 

Irrational numbers arising from certain differential equations, (with M. Ram Murty), Canadian Math. Bull. 20 (1977) 117-120.

2. 

Some results in number theory I, (with Ram Murty) Acta Arith. 35 (1979) 367-371.

3. 

On the Sato Tate conjecture, Number Theory related to Fermat's last Theorem, ed. N. Koblitz, Birkhauser-Verlag, Boston, (1982) 195-205.

4. 

Algebraic cycles on abelian varieties, Duke Math J. 50 (1983) 487-504.

5. 

On the density of various classes of groups, (with Ram Murty), J. Number Theory 17 (1983) 29-36.

6. 

Counting finite groups, (with M. Ram Murty), preprint, 1983.

7. 

Exceptional Hodge classes on certain abelian varieties, Math. Annalen 268 (1984) 197-206.

8. 

Fourier coefficients of modular forms, Proceedings of Matscience Number Theory conference, Lecture Notes in Mathematics 1122, 163-172.

9. 

Prime divisors of Fourier coefficients of modular forms, (with M. Ram Murty) Duke Math. J. 51 (1984) 57-77.

10. 

The number of groups of a given order, (with M. Ram Murty), J. Number Theory 18 (1984) 178-191.

11. 

On groups of squarefree order, (with M. Ram Murty), Math. Annalen 267 (1984) 1090-1101.

12. 

An analogue of the Erdos-Kac theorem for Fourier coefficients of modular forms, (with M. Ram Murty), Indian J. Pure and Appl. Math. 15 (10) (1984) 1090-1101.

13. 

Explicit formulae and the Lang-Trotter conjecture, Rocky Mountain J. Math. 15 (2) (1985) 535-551.

14. 

A variant of the Bombieri-Vinogradov theorem (with M. Ram Murty) CMS Conference proceedings, 7 (1987) 243-272.

15. 

Period relations and Tate's conjecture for Hilbert modular surfaces, (with D. Ramakrishnan), Inventiones Math. 89 (1987) 319-345.

16. 

On the enumeration of finite groups, (with M. Ram Murty and P. Erdos). J. Number Theory 25 (1987) 360-378.

17. 

Odd values of the Ramanujan t Function, (with M. Ram Murty and T.N. Shorey), Bulletin Math. Soc. France 115 (1987) 391-395.

18. 

The Euclidean algorithm for S-integers (with M. Ram Murty and Rajiv Gupta), CMS Conference Proceedings 7 (1987) 189-201.

19. 

The Hodge group of an abelian variety, Proc. Amer. Math. Soc. 104 (1) (1988) 61-68.

20. 

Modular forms and the Chebotarev density theorem, (with M. Ram Murty and N. Saradha), Amer. Journal of Math. 110 (1988) 253-281.

21. 

Lacunarity and modular forms, J. Indian Math. Soc., 57 (1988) 127-146.

22. 

The Manin-Drinfeld theorem and Ramanujan sums, (with D. Ramakrishnan), Proc. Indian Acad. Sci. 97 (1988) 251-262.

23. 

Zeros and poles of Artin L-functions, (with R. Foote), Math. Proc. Camb. Phil. Soc. 105 (1989) 5-11.

24. 

Holomorphy of Artin L-functions, in: Proc. Intl. Conf. on Ramanujan, Ramanujan Mathematical Society, 1989, pp. 11-24.

25. 

Non-vanishing of L-functions and their derivatives, Proc. Montreal Conf. on modular forms, (ed. R. Murty) Univ. of Montreal Press, 1990, pp. 89-113.

26. 

Computing the Hodge group of an abelian variety, in: Seminaire de theorie de Nombres Paris, (ed. C. Goldstein) Birkhauser-Verlag 1990, pp. 141-158.

27. 

Mean values of derivatives of modular L-functions, (with M. Ram Murty) Annals of Math. 133 (1991) 447-475.

28. 

Zeros of Dirichlet L-functions , (with R. Balasubramanian), Ann. Scient. Ecole Norm. Sup., 25 (1992), 567-615.

29. 

The Albanese variety of a unitary Shimura variety (with D. Ramakrishnan), in: The Zeta Functions of Picard Modular Surfaces, (ed. R. Langlands, D. Ramakrishnan), CRM (1992) 445-464.

30. 

Base change and the Birch and Swinnerton-Dyer conjecture, (with M. Ram Murty) Papers in Honor of E. Grosswald, ed. M. Knopp, Contemporary Math. 143 (1993), 481-494.

31. 

The notion of a Shimura variety, in: Advances in Number Theory, ed. F. Gouvea and N. Yui, Oxford University Press, 1993, pp. 195-212.

32. 

Ramanujan and Harish-Chandra, Math. Intelligencer, 15 (1993), 33-39.

33. 

Strong multiplicity one for Selberg's Class, (with M. Ram Murty), C.R. Acad. Sci. (Paris), 319 (1994), 315-320.

34. 

Effective versions of the Chebotarev density theorem for function fields, (with J. Scherk), C.R. Acad. Sci. (Paris), 319 (1994), 523-528.

35. 

Report on Fermat's Last Theorem, Current Science, 67 (2) (1994), 82-88.

36. 

The least prime which does not split completely, Forum Mathematicum, 6 (1994), pp. 555-565.

37. 

Modular elliptic curves, in: Seminar on Fermat's Last Theorem, ed. K. Murty, pp. 1-38, CMS Conf. Proc. vol. 17, AMS, 1995.

38. 

Bounded and finite generation of arithmetic groups, in: Number Theory, ed. K. Dilcher, pp. 249-261, CMS Conf. Proc. vol. 15, AMS, 1995.

39. 

Fermat's Last Theorem, in: Analysis, Geometry and Probability, pp. 125-139, ed. R. Bhatia, Hindustan Book Agency, New Delhi, 1996.

40. 

Modular forms and the Chebotarev Density Theorem, II, in: Analytic Number Theory, pp. 287-308, ed. Y. Motohashi, London Math. Soc. Lecture Notes 247, Cambridge Univ. Press, 1997.

41. 

Frobenius distributions and Galois representations, in: Automorphic Forms, Automorphic Representations and Arithmetic, ed. R. Doran, Z.-L. Dou and G. Gilbert, pp. 193-211, Proc. Symp. Pure Math. Vol. 66, Part 1, Amer. Math. Soc., Providence, 1999.

42. 

Stark zeros in certain towers of fields, Math. Res. Letters, 6(1999), 511-520.

43. 

A Tauberian estimate for sums of coefficients of Dirichlet series, Comptes Rendus Math. Rep. Acad. Sci. Canada, 21(1999), 153-159.

44. 

Tate cycles on a product of two Hilbert modular surfaces, (with D. Prasad), J. Number Theory, 80(2000), 25-43.

45. 

Hodge and Weil classes on Abelian varieties, in: The Arithmetic and Geometry of Algebraic Cycles, pp. 83-115, eds. B. Gordon, J. Lewis and N. Yui, Kluwer Academic Publishers, Amsterdam, 2000.

46. 

Average values of quadratic twists of modular L-functions, (with T. Stefanicki), Func. et. Approx., 28(2000), 155-172.

47. 

The work of Sarvadaman Chowla, (with M. Ram Murty and K. S. Williams), pp. 7-25, in: The Collected Works of S. Chowla, eds. J. Huard and K. Williams, CRM, Montreal, 2000.

48.  The least prime in a conjugacy class, Comptes Rendus Math. Rep. Acad. Sci. Canada, 22(4)(2000), 129-146.

49.  Abelian varieties - optimal cryptography for wireless communications?, Wireless Security Perspectives, 2(2000), 3-5.

50. 

Descending rational points on elliptic curves to smaller fields, (with A. Akbary), Canadian J. Math., 53(2001), 449-469.

51. 

Class numbers of CM-fields with solvable normal closure, Compositio Math., 127(2001), 273-287.

52. 

Splitting of primes in infinite extensions, to appear in the Proceedings of the Millenial Conference on Number Theory, 2001, ed. A. Hildebrand, B. Berndt and N. Boston.

53.  An application of sieve methods to elliptic curves, (with S. Ali Miri), to appear in proceedings of Indocrypt 2001, Lecture Notes in Computer Science, Springer.

54.  The addition law on hyperelliptic Jacobians, to appear in Proc. of Allahabad Conf. on Number Theory, 2001.

55.  Estimates for sums of coefficients of Dirichlet series with functional equation, preprint, 2001.

56. 

Satake compactifications and the congruence subgroup problem, (with J. Scherk), preprint, 2001.

57. 

Bounded generation for SL_n (n ³ > 1) and Sp_2n  (n ³ > 1) , (with D. Loukanidis), to be submitted.

58. 

Semiregular cycles on Abelian varieties, in preparation.

59. 

Pair correlation and the Chebotarev density theorem, (with M. Ram Murty), in preparation.

60. 

Splitting of Abelian varieties, (with V. Patankar), in preparation.

61. 

Frobenius distributions and Galois representations: Numerical evidence, (with K. James and C. Mehta), in preparation.

62. 

Elliptic curve discrete logarithm problem and the lifting problem, (with S. Ali Miri), in preparation.

1. 

Introduction to Abelian varieties, CRM Monograph Series Volume 3, Amer. Math. Soc., Providence, 1993. (112 pages).

2.

Seminar on Fermat's Last Theorem , ed. K. Murty, CMS Conf. Proc. vol. 17, AMS, 1995. (265 pages)

3. 

Non-vanishing of L-functions and applications (with M. Ram Murty), Progress in Math. 157, Birkhauser, Basel, 1997. (196 pages)

4. 

Number Theory, ed. V. Kumar Murty and M. Waldschmidt, Contemporary Mathematics 210, Amer. Math. Soc., Providence, 1998. (399 pages)

5. 

Computational aspects of Number theory, (with S. Ali Miri), in preparation.