### Sort by:

Title Co-author Year Subject### Publications By Subject

### Algebraic Geometry

The Manin-Drinfeld theorem and Ramanujan suma

with Ramakrishnan, D.*Proc. Indian Acad. Sci. 97 (*

**1988**) 251-262The Albanese variety of a unitary Shimura variety

with Ramakrishnan, D.*The Zeta Functions of Picard Modular Surfaces, ed. R. Langlands, D Ramakrishnan, CRM (*

**1992**) 445-464Period relations and Tate's conjecture for Hilbert modular surfaces

with Ramakrishnan, D.*Inventiones Math 89 (*

**1987**) 319-345Semiregularity and Abelian varieties

*Special volume in honour of S Bloch, Fields Institute Communications, Volume 56, American Math Society, Providence (*

**2009**) 293-305Exceptional Hodge classes on certain abelian varieties

*Math. Annalen, 268 (*

**1984**) 197-206The Hodge group of an abelian variety

*Proc. Amer. Math. Soc. 104 (1) (*

**1988**) 61-68Algebraic cycles on abelian varieties

*Duke Math J. 50 (*

**1983**) 487-504Hodge and Weil classes on Abelian varieties

*The Arithmetic and Geometry of Algebraic Cycles, eds B. Gordon, J. Lewis and N. Yui, Kluwer Academic Publishers, Amsterdam (*

**2000**) 83-115Tate cycles on a product of two Hilbert modular sutface

with Prasad, D.*J Number Theory, 80 (*

**2000**) 25-43Computing the Hodge group of an Abelian variety

*Seminaire de theorie de Nombres Paris, ed. C Goldstein, Birkhauser-Verlag (*

**1990**) 141-158### Algebraic Number Theory

Distribution of values of $\frac{L'}{L} (\sigma, \chi_D)$

with Mourtada, M.*Moscow Math J. (to appear) (*

**2013**)Bounded and finite generation of arithmetic groups

*CMS Conf. Proc., vol. 15, Number theory, ed. K. Dilcher, AMS (*

**1995**) 249-261The field of Fourier coefficients of a modular form

*Ramanujan Mathematical Society Volume in Honour of T. C. Vasudevan, RMS, Chennai (*

**2011**) 103-111Frobenius distributions and Galois representations

*Proc. Symp. Pure Math., vol 66, part 1, Automorphic Forms, Automorphic Representations and Arithmetic, ed. R. Doran, Z-L. Dou, G. Gilbert, Amer. Math. Soc., Providence (*

**1999**) 193-211Modular forms and the Chebotarev Density Theorem, II

*Analytic Number Theory, ed. Y. Motohashi, London Math. Soc. Lecture Notes 247, Cambridge Univ. Press (*

**1997**) 287-308Class numbers of CM fields with solvable normal closure

*Compositio Math, 127 (*

**2001**) 273-287A Tauberian estimate for sums of coefficients of Dirichlet series

*Comptes Rendus Math. Rep. Acad. Sci. Canada, 21 (*

**1999**) 153-159Splitting of primes in infinite extensions

*Proceedings of the Millenial Conference on Number Theory, eds. A. Hildebrand, B. Berndt and N. Boston, A.K. Peters, Boston (*

**2001**) 23-41The fundamental group of the reductive Borel-Serre and Satake compactifications

with Ji, L., Saper, L., and Scherk, J.*Asian J. Math., 19 (*

**2015**) 465-486Stark zeros in certain towers of fields

*Math Res. Letters, 6 (*

**1999**) 511-520Modular forms and the Chebotarev density theorem

with Murty, Ram M., and Saradha, N.*Amer. Journal of Math. 110 (*

**1988**) 253-281The least prime in a conjugacy class

*Comptes Rendus Math. Rep. Acad. Sci. Canada, 22(4) (*

**2000**) 129-146The Euclidean algorithm for $S$-integers

with Murty, Ram M., and Gupta, R.*CMS Conference Proceedings 7 (*

**1987**) 189-201The growth of the Selmer group of an elliptic curve with split multiplicative reduction

with Lim, M. Fai*Intl J Number Theory, 10 (*

**2014**) 675-687### Analytic Number Theory

An analogue of the Siegel Walfisz theorem for the cyclicity of CM elliptic curves mod p

with Akbary, A.*Indian J Pure Appl Math, 41 (*

**2010**) 25-37Ramanujan and prime numbers

*The Legacy of Srinivasa Ramanujan, eds. B Berndt and D Prasad, RMS Lecture Notes 20, Ramanujan Mathematical Society, Chennai (*

**2013**) 281-299The least prime which does not split completely

*Forum Mathematicum, 6 (*

**1994**) 555-565The Euler-Kronecker constant of a cyclotomic field

*Annales des Sciences Mathematiques du Quebec, 35 (*

**2011**) 239-247Average Values of quadratic twists of modular $L$-functions

with Stefanicki, T.*Func. et. Approx., 28 (*

**2000**) 155-172Some results in number theory, II

*Number theory, eds. S Adhikari, R Balasubramanian, K Srinivas, Ramanujan Math. Soc. Lecture Notes, 1 (*

**2005**) 51-55On the logarithmic derivatives of Dirichlet L functions at s=1

with Ihara, Y., and Shimura, M.*Acta Arithmetica, 137 (*

**2009**) 253-276Holomorphy of Artin $L$-functions

*Proc. Intl. Conf. on Ramanujan, Ramanujan Mathematical Society (*

**1989**) 11-24Mean values of derivatives of modular $L$-functions

with Murty, Ram M.*Annals of Math. 133 (*

**1991**) 447-475Zeros of Dirichlet $L$-functions

with Balasubramanian, R.*Ann. Scient. Ecole Norm. Sup., 25 (*

**1992**) 567-615The Lindelof class of L functions

*The conference on L functions, eds L Weng and M Kaneko, World Scientific (*

**2007**) 165-174Some results in number theory I

with Murty, Ram M.*Acta Arith. 35 (*

**1979**) 367-371A variant of Lehmer's conjecture

*J Number Theory, 123 (*

**2007**) 80-91Non-vanishing of $L$-functions and their derivatives

*Proc. Montreal Conf. on modular forms, ed. R. Murty, Univ of Montreal Press (*

**1990**) 89-113On a conjecture of Lang and Trotter

with Akbary, A., and Ghioca, D.*Math Annalen, 347 (*

**2010**) 365-394A variant of Lehmer's conjecture II: The CM case

with Gun, S.*Canadian J Math, 63 (*

**2011**) 298-326A variant of the Lang-Trotter conjecture

with Murty, Ram M.*Number Theory, Analysis and Geometry: In memory of Serge Lang, eds. D Ramakrishnan et. al., Springer (*

**2011**) 461-474Transcendental values of class group L-functions

with Murty, Ram M.*Math Annalen, 351 (*

**2011**) 835-855Omega theorems for $\frac{L'}{L} (1, \chi_D)$

with Mourtada, M.*Intl J Number Theory, 9 (*

**2013**) 561-581Zeros and poles of Artin $L$-functions

with Foote, R.*Math. Proc. Camb. Phil. Soc. 105 (*

**1989**) 5-11On the Sato-Tate conjecture II

*On Certain L-functions: A Volume in honour of F. Shahidi, Clay Mathematics Proceedings 43, Amer. Math. Soc., Providence (*

**2011**) 471-482A variant of the Bombieri Vinogradov theorem

with Murty, Ram M.*CMS Conference proceedings, 7 (*

**1987**) 243-272Strong multiplicity one for Selberg's Class

with Murty, Ram M.*C.R. Acad. Sci., 319, Paris (*

**1994**) 315-320An examination of identity management models in an internet setting

with Giuliani, K.*Cyber Security, Cyber Crime and Cyber Forensics: Applications and Perspectives eds. R. Santanam, M. Sethumadhavan, M. Virendra, IGI Global Press, Pennsylvania (*

**2011**) 106-114Explicit formulae and the Lang-Trotter conjecture

*Rocky Mountain J. Math. 15 (2) (*

**1985**) 535-551The Sato-Tate conjecture and generalizations

with Murty, Ram M.*Current Trends in Science: Platinum Jubilee Special of the Indian Academy of Sciences, ed. N. Mukunda, Indian Academy of Sciences, Bangalore (*

**2009**) 639-646### Arithmetic Geometry

An analogue of the Siegel Walfisz theorem for the cyclicity of CM elliptic curves mod p

with Akbary, A.*Indian J Pure Appl Math, 41 (*

**2010**) 25-37A growth of Selmer ranks of an Abelian variety with complex multiplication

with Ouyang, Y.*Pure and Appl Math Quarterly, 2 (*

**2006**) 539-555Tate cycles on Abelian varieties with complex multiplication

with Patankar, V.*Canadian J. Math., 67 (*

**2015**) 198-213Growth of Selmer groups of CM Abelian varieties

with Lim, M. Fai*Canadian J. Math, 67 (*

**2015**) 654-666Effective versions of the Chebotarev density theorem for function fields

with Scherk, J.*C.R. Acad. Sci., 319, Paris (*

**1994**) 523-528On the Sato-Tate conjecture

*Number Theory related to Fermat's last Theorem, ed. N. Koblitz, Birkhauser-Verlag, Boston (*

**1982**) 195-205Splitting of Abelian varieties: a new local global problem

*Algebra and Number Theory, ed. R. Tandon, Hindustan Book Agency, New Dehli (*

**2005**) 258-268Modular elliptic curves

*CMS Conf. Proc. vol. 17, Seminar on Fermat's Last Theorem, ed. K. Murty, AMS (*

**1995**) 1-38Descending rational points on elliptic curves to smaller fields

with Akbary, A.*Canadian J. Math., 53 (*

**2001**) 449-469Splitting of Abelian varieties

with Patankar, V.*Intl Math Res Not, article ID rnn033, doi: 10.1093/imrn /rnn033 (*

**2008**) 27 pagesBase change and the Birch and Swinnerton-Dyer conjecture

with Murty, Ram M.*Contemporary Math., 143 (Papers in Honor of E. Grosswald), ed. M. Knopp (*

**1993**) 481-494Splitting of Abelian varieties II: Elliptic Dynkin Pairs

with Zong, Y.*(submitted) (*

**2014**)Reduction mod p of subgroups of the Mordell Weil group of an elliptic curve

with Akbary, A.*Intl J Number Theory, 5 (*

**2009**) 1-23An examination of identity management models in an internet setting

with Giuliani, K.*Cyber Security, Cyber Crime and Cyber Forensics: Applications and Perspectives eds. R. Santanam, M. Sethumadhavan, M. Virendra, IGI Global Press, Pennsylvania (*

**2011**) 106-114The growth of the Selmer group of an elliptic curve with split multiplicative reduction

with Lim, M. Fai*Intl J Number Theory, 10 (*

**2014**) 675-687### Automorphic Forms

Lacunarity and modular forms

*J. Indian Math. Soc., 57 (*

**1988**) 127-146The field of Fourier coefficients of a modular form

*Ramanujan Mathematical Society Volume in Honour of T. C. Vasudevan, RMS, Chennai (*

**2011**) 103-111Prime divisors of Fourier coefficients of modular forms

with Murty, Ram M.*Duke Math. J. 51 (*

**1984**) 57-77An analogue of the Erdos-Kac theorem for Fourier coefficients of modular forms

with Murty, Ram M.*Indian J. Pure and Appl. Math. 15 (10) (*

**1984**) 1090-1101Estimates for sums of coefficients of Dirichlet series with functional equation

*The Ramanujan Journal, 7 (*

**2003**) 225-235Odd values of the Ramanujan $\tau$ Function

with Murty, Ram M., and Shorey, T.N.*Bulletin Math. Soc. France 115 (*

**1987**) 391-395Fourier coefficients of forms of CM type

with Laptyeva, N.*Indian J. Pure Appl. Math., 45 (*

**2014**) 747-758On a conjecture of Lang and Trotter

with Akbary, A., and Ghioca, D.*Math Annalen, 347 (*

**2010**) 365-394A variant of Lehmer's conjecture II: The CM case

with Gun, S.*Canadian J Math, 63 (*

**2011**) 298-326A variant of the Lang-Trotter conjecture

with Murty, Ram M.*Number Theory, Analysis and Geometry: In memory of Serge Lang, eds. D Ramakrishnan et. al., Springer (*

**2011**) 461-474On the Sato-Tate conjecture II

*On Certain L-functions: A Volume in honour of F. Shahidi, Clay Mathematics Proceedings 43, Amer. Math. Soc., Providence (*

**2011**) 471-482The Sato-Tate conjecture and generalizations

with Murty, Ram M.*Current Trends in Science: Platinum Jubilee Special of the Indian Academy of Sciences, ed. N. Mukunda, Indian Academy of Sciences, Bangalore (*

**2009**) 639-646### Cryptography

A privacy preserving e-payment architecture

with Plateaux, A., Coquet, V., Vernois, S., Lacharme, P., and Rosenberger, C.*Lecture Notes in Computer Science, 7859, Springer-Verlag, Heidelberg (*

**2013**) 402Online user's registration respecting privacy

with Plateaux, A., Lacharme, P., and Rosenberger, C.*International Conference on Mobile Applications and Security Management, DOI: 10.1109/WCCIT.2013.6618718, IEEE, 2013 (*

**2013**) 1-5Cryptosystems arising from Abelian varieties

*Handbook of Finite Fields, eds. G. Mullen and D. Panario, CRC Press, Boca Raton (*

**2013**) 803-811Security and authentication for networked storage

with Xu, G.*SECRYPT, eds. E. Fernandez Medina et. al., INSTICC Press, Portugal (*

**2008**) 477-480ERINDALE: A polynomial based hashing algorithm

with Volkovs, N.*Lecture Notes in Computer Science 5557, Springer Verlag, Berlin, International Workshop on Coding and Cryptographyeds. eds. C Xing et al (*

**2009**) 157-170An e-payment architecture ensuring a high level of privacy protection

with Plateaux, A., Lacharme, P., Coquet, V., Vernois, S., and Rosenberger, C.*Security and Privacy in Communication Networks, Lecture Notes of the Institute for Computer Science, Social Informatics and Telecommunications Engineering, 127 (*

**2013**) 305-322Nonadjacent radix tau expansions of integers in Euclidean imaginary quadratic number fields

with Blake, I., and Xu, G.*Canadian J Math, 60 (*

**2008**) 1267-1282Non linear secret sharing and prime numbers

with Xu, G.*Discrete Mathematics and Applications, ed. M Sethumadhavan, Narosa Publishing, Chennai (*

**2005**) 1-10Efficient algorithms for Koblitz curves over fields of characteristics three

with Blake, I., and Xu, G.*J. Discrete Algorithms (*

**2005**) 113-124An application of sieve methods to elliptic curves

with Ali Miri, S.*Lecture Notes in Computer Science 2247, INDOCRYPT 2001, eds. C. Pandu Rangan, C. Ding, Springer Verlag, Berlin (*

**2001**) 91-98Refinements of Millers algorithms for computing the Weil Tate pairing

with Blake, I., and Xu, G.*J. Algorithms (*

**2006**) 134-149A polynomial based hashing algorithm

with Volkovs, N.*SECRYPT 2008 International Conference on Security and Cryptography, eds. E Fernandez Medina et. al. INSTICC Press, Portugal (*

**2008**) 103-106Counting points on an Abelian variety over a finite field

with Izadi, F.A.*Lecture Notes in Computer Science 2904, INDOCRYPT 2003, eds. T Johansson, S Maitra, Springer-Verlag, Berlin (*

**2004**) 323-333The addition law on hyperelliptic Jacobians

*Current Trends in Number Theory, eds. S Adhikari, S A Katre, B Ramakrishnan, Hindustan Book Agency, New Delhi (*

**2002**) 101-110A contactless e-health information system with privacy

with Plateaux, A., Lacharme, P., and Rosenberger, C.*Wireless Communications and Mobile Computing Conference, DOI: 10.1109/IWCMC.2013.6583805, IEEE (*

**2013**) 1660-1665A note on the Window $\tau$-NAF algorithm

with Blake, I., and Xu, G.*Information Processing Letters, 95 (*

**2005**) 496-502Abelian varieties - optimal cryptography for wireless communications?

*Wireless Security Perspectives, 2 (*

**2000**) 3-5Abelian varieties and cryptography in INDOCRYPT

*Lecture Notes in Computer Science, 3797, ed. C. Veni Madhavan (*

**2005**) 1-12An examination of identity management models in an internet setting

with Giuliani, K.*Cyber Security, Cyber Crime and Cyber Forensics: Applications and Perspectives eds. R. Santanam, M. Sethumadhavan, M. Virendra, IGI Global Press, Pennsylvania (*

**2011**) 106-114Algebraic curves and cryptography

*Fields Institute Communications 53, Amer. Math. Soc., Providence (*

**2010**) 133 pages### Expository

Ramanujan and Harish-Chandra

*Math. Intelligencer, 15 (*

**1993**) 33-39The notion of a Shimura variety

*Advances in Number Theory, ed. F. Gouvea, N. Yui, Oxford University Press (*

**1993**) 195-212Fermat's Last Theorem

*Analysis, Geometry and Probability, ed. R. Bhatia, Hindustan Book Agency, New Delhi (*

**1996**) 125-139The work of Sarvadaman Chowla

with Murty, Ram M., and Williams, K.S.*The Collected Works of S Chowla, ed. J. Huard and K. Williams, CRM, Montreal (*

**2000**) 7-25Report on Fermat's Last Theorem

*Current Sceience, 67 (2) (*

**1994**) 82-88### Group Theory

On the density of various classes of croups

with Murty, Ram M.*J. Number Theory 17 (*

**1983**) 29-36On groups of squarefree order

with Murty, Ram M.*Math. Annalen 267 (*

**1984**) 1090-1101On the enumeration of finite groups

with Murty, Ram M., and Erdos, P.*J. Number Theory 25 (*

**1987**) 360-378The number of groups of a given order

with Murty, Ram M.*J. Number Theory 18 (*

**1984**) 178-191### Topology

The fundamental group of the reductive Borel-Serre and Satake compactifications

with Ji, L., Saper, L., and Scherk, J.*Asian J. Math., 19 (*

**2015**) 465-486### Transcendental Number Theory

On a conjecture of Shorey

with Murty, Ram M.*Diophanatine Equations, ed. N. Saradha, Narosa, New Delhi (*

**2008**) 167-176Irrational numbers arising from certain differential equations

with Murty, Ram M.*Canadian Math. Bull. 20 (*

**1977**) 117-120On a problem of Ruderman

with Murty, Ram M.*Amer. Math. Monthly, 118 (*

**2011**) 644-650Transcendental values of class group L functions II

with Murty, Ram M.*Proc. Amer. Math. Soc., 140 (*

**2012**) 3041-3047On transcendence of generalized Euler Lehmer constants II

with Gun, S., and Saha, E.*(*

**2014**)Transcendental values of class group L-functions

with Murty, Ram M.*Math Annalen, 351 (*

**2011**) 835-855A problem of Chowla revisited

with Murty, Ram M.*J Number Theory, 131 (*

**2011**) 1723-1733Odd values of Fourier coefficients of certain modular forms

with Murty, Ram M.*Intl J Number Theory (*

**2007**) 455-470### Other

A note on diagonal and Hermitian hyper surfaces

with Blake, I., and Usefi, H.*submitted (*

**2014**)Counting finite groups

with Murty, Ram M.*preprint (*

**1983**)Splitting of Abelian varieties

with Zong, Y.*Advances in Mathematics of Communication, 8 (*

**2014**) 511-519Heilbronn Characters

with Foote, R., and Ginsburg, H.*Bulletin of the Amer. Math. Soc., 52 (*

**2015**) 465-496