# Publications

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Title Co-author Year Subject

### 2010-

• 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) 25-37
• Ramanujan and prime numbers

The Legacy of Srinivasa Ramanujan, eds. B Berndt and D Prasad, RMS Lecture Notes 20, Ramanujan Mathematical Society, Chennai (2013) 281-299
• Distribution of values of $\frac{L'}{L} (\sigma, \chi_D)$

Moscow Math J. (to appear) (2013)
• 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) 402
• A note on diagonal and Hermitian hyper surfaces

with Blake, I., and Use fi, H.
submitted (2014)
• The Euler-Kronecker constant of a cyclotomic field

Annales des Sciences Mathematiques du Quebec, 35 (2011) 239-247
• Online 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) 1-5
• Cryptosystems arising from Abelian varieties

Handbook of Finite Fields, eds. G. Mullen and D. Panario, CRC Press, Boca Raton (2013) 803-811
• The field of Fourier coefficients of a modular form

Ramanujan Mathematical Society Volume in Honour of T. C. Vasudevan, RMS, Chennai (2011) 103-111
• Tate cycles on Abelian varieties with complex multiplication

with Patankar, V.
Canadian J. Math., 67 (2015) 198-213
• Growth of Selmer groups of CM Abelian varieties

with Lim, M. Fai
Canadian J. Math, 67 (2015) 654-666
• An 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) 305-322
• 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
• On a problem of Ruderman

with Murty, Ram M.
Amer. Math. Monthly, 118 (2011) 644-650
• Transcendental values of class group L functions II

with Murty, Ram M.
Proc. Amer. Math. Soc., 140 (2012) 3041-3047
• Fourier coefficients of forms of CM type

with Laptyeva, N.
Indian J. Pure Appl. Math., 45 (2014) 747-758
• On a conjecture of Lang and Trotter

with Akbary, A., and Ghioca, D.
Math Annalen, 347 (2010) 365-394
• A variant of Lehmer's conjecture II: The CM case

with Gun, S.
Canadian J Math, 63 (2011) 298-326
• Splitting of Abelian varieties II: Elliptic Dynkin Pairs

with Zong, Y.
(submitted) (2014)
• On transcendence of generalized Euler Lehmer constants II

with Gun, S., and Saha, E.
(2014)
• A 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) 461-474
• Splitting of Abelian varieties

with Zong, Y.
Advances in Mathematics of Communication, 8 (2014) 511-519
• Transcendental values of class group L-functions

with Murty, Ram M.
Math Annalen, 351 (2011) 835-855
• Omega theorems for $\frac{L'}{L} (1, \chi_D)$

Intl J Number Theory, 9 (2013) 561-581
• Heilbronn Characters

with Foote, R., and Ginsburg, H.
Bulletin of the Amer. Math. Soc., 52 (2015) 465-496
• A problem of Chowla revisited

with Murty, Ram M.
J Number Theory, 131 (2011) 1723-1733
• A 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) 1660-1665
• On 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) 471-482
• An 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) 106-114
• The 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
• Algebraic curves and cryptography

Fields Institute Communications 53, Amer. Math. Soc., Providence (2010) 133 pages

### 2000-2009

• A growth of Selmer ranks of an Abelian variety with complex multiplication

with Ouyang, Y.
Pure and Appl Math Quarterly, 2 (2006) 539-555
• Average Values of quadratic twists of modular $L$-functions

with Stefanicki, T.
Func. et. Approx., 28 (2000) 155-172
• Security and authentication for networked storage

with Xu, G.
SECRYPT, eds. E. Fernandez Medina et. al., INSTICC Press, Portugal (2008) 477-480
• On a conjecture of Shorey

with Murty, Ram M.
Diophanatine Equations, ed. N. Saradha, Narosa, New Delhi (2008) 167-176
• ERINDALE: 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) 157-170
• Some results in number theory, II

Number theory, eds. S Adhikari, R Balasubramanian, K Srinivas, Ramanujan Math. Soc. Lecture Notes, 1 (2005) 51-55
• On the logarithmic derivatives of Dirichlet L functions at s=1

with Ihara, Y., and Shimura, M.
Acta Arithmetica, 137 (2009) 253-276
• The 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) 7-25
• Semiregularity and Abelian varieties

Special volume in honour of S Bloch, Fields Institute Communications, Volume 56, American Math Society, Providence (2009) 293-305
• Splitting of Abelian varieties: a new local global problem

Algebra and Number Theory, ed. R. Tandon, Hindustan Book Agency, New Dehli (2005) 258-268

with Blake, I., and Xu, G.
Canadian J Math, 60 (2008) 1267-1282
• Descending rational points on elliptic curves to smaller fields

with Akbary, A.
Canadian J. Math., 53 (2001) 449-469
• Splitting of Abelian varieties

with Patankar, V.
Intl Math Res Not, article ID rnn033, doi: 10.1093/imrn /rnn033 (2008) 27 pages
• Class numbers of CM fields with solvable normal closure

Compositio Math, 127 (2001) 273-287
• Splitting 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) 23-41
• Estimates for sums of coefficients of Dirichlet series with functional equation

The Ramanujan Journal, 7 (2003) 225-235
• The Lindelof class of L functions

The conference on L functions, eds L Weng and M Kaneko, World Scientific (2007) 165-174
• Non linear secret sharing and prime numbers

with Xu, G.
Discrete Mathematics and Applications, ed. M Sethumadhavan, Narosa Publishing, Chennai (2005) 1-10
• A variant of Lehmer's conjecture

J Number Theory, 123 (2007) 80-91
• Efficient algorithms for Koblitz curves over fields of characteristics three

with Blake, I., and Xu, G.
J. Discrete Algorithms (2005) 113-124
• An 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) 91-98
• Hodge 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) 83-115
• The least prime in a conjugacy class

• Refinements of Millers algorithms for computing the Weil Tate pairing

with Blake, I., and Xu, G.
J. Algorithms (2006) 134-149
• A 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) 103-106
• Tate cycles on a product of two Hilbert modular sutface

J Number Theory, 80 (2000) 25-43
• Counting points on an Abelian variety over a finite field

Lecture Notes in Computer Science 2904, INDOCRYPT 2003, eds. T Johansson, S Maitra, Springer-Verlag, Berlin (2004) 323-333
• The addition law on hyperelliptic Jacobians

Current Trends in Number Theory, eds. S Adhikari, S A Katre, B Ramakrishnan, Hindustan Book Agency, New Delhi (2002) 101-110
• Reduction mod p of subgroups of the Mordell Weil group of an elliptic curve

with Akbary, A.
Intl J Number Theory, 5 (2009) 1-23
• Odd values of Fourier coefficients of certain modular forms

with Murty, Ram M.
Intl J Number Theory (2007) 455-470
• A note on the Window $\tau$-NAF algorithm

with Blake, I., and Xu, G.
Information Processing Letters, 95 (2005) 496-502
• Abelian varieties - optimal cryptography for wireless communications?

Wireless Security Perspectives, 2 (2000) 3-5
• Abelian varieties and cryptography in INDOCRYPT

Lecture Notes in Computer Science, 3797, ed. C. Veni Madhavan (2005) 1-12
• The 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

### 1990-1999

• The least prime which does not split completely

Forum Mathematicum, 6 (1994) 555-565
• Ramanujan and Harish-Chandra

Math. Intelligencer, 15 (1993) 33-39
• Bounded and finite generation of arithmetic groups

CMS Conf. Proc., vol. 15, Number theory, ed. K. Dilcher, AMS (1995) 249-261
• The Albanese variety of a unitary Shimura variety

with Ramakrishnan, D.
The Zeta Functions of Picard Modular Surfaces, ed. R. Langlands, D Ramakrishnan, CRM (1992) 445-464
• Frobenius 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) 193-211
• The notion of a Shimura variety

Advances in Number Theory, ed. F. Gouvea, N. Yui, Oxford University Press (1993) 195-212
• Fermat's Last Theorem

Analysis, Geometry and Probability, ed. R. Bhatia, Hindustan Book Agency, New Delhi (1996) 125-139
• Effective versions of the Chebotarev density theorem for function fields

with Scherk, J.
C.R. Acad. Sci., 319, Paris (1994) 523-528
• Modular forms and the Chebotarev Density Theorem, II

Analytic Number Theory, ed. Y. Motohashi, London Math. Soc. Lecture Notes 247, Cambridge Univ. Press (1997) 287-308
• Modular elliptic curves

CMS Conf. Proc. vol. 17, Seminar on Fermat's Last Theorem, ed. K. Murty, AMS (1995) 1-38
• Mean values of derivatives of modular $L$-functions

with Murty, Ram M.
Annals of Math. 133 (1991) 447-475
• A Tauberian estimate for sums of coefficients of Dirichlet series

• Zeros of Dirichlet $L$-functions

with Balasubramanian, R.
Ann. Scient. Ecole Norm. Sup., 25 (1992) 567-615
• Base 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) 481-494
• Stark zeros in certain towers of fields

Math Res. Letters, 6 (1999) 511-520
• Non-vanishing of $L$-functions and their derivatives

Proc. Montreal Conf. on modular forms, ed. R. Murty, Univ of Montreal Press (1990) 89-113
• Report on Fermat's Last Theorem

Current Sceience, 67 (2) (1994) 82-88
• Strong multiplicity one for Selberg's Class

with Murty, Ram M.
C.R. Acad. Sci., 319, Paris (1994) 315-320
• Computing the Hodge group of an Abelian variety

Seminaire de theorie de Nombres Paris, ed. C Goldstein, Birkhauser-Verlag (1990) 141-158

### 1980-1989

• Lacunarity and modular forms

J. Indian Math. Soc., 57 (1988) 127-146
• The Manin-Drinfeld theorem and Ramanujan suma

with Ramakrishnan, D.
Proc. Indian Acad. Sci. 97 (1988) 251-262
• Prime divisors of Fourier coefficients of modular forms

with Murty, Ram M.
Duke Math. J. 51 (1984) 57-77
• On the density of various classes of croups

with Murty, Ram M.
J. Number Theory 17 (1983) 29-36
• Period relations and Tate's conjecture for Hilbert modular surfaces

with Ramakrishnan, D.
Inventiones Math 89 (1987) 319-345
• On groups of squarefree order

with Murty, Ram M.
Math. Annalen 267 (1984) 1090-1101
• An 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) 1090-1101
• Counting finite groups

with Murty, Ram M.
preprint (1983)
• On the Sato-Tate conjecture

Number Theory related to Fermat's last Theorem, ed. N. Koblitz, Birkhauser-Verlag, Boston (1982) 195-205
• Holomorphy of Artin $L$-functions

Proc. Intl. Conf. on Ramanujan, Ramanujan Mathematical Society (1989) 11-24
• Exceptional Hodge classes on certain abelian varieties

Math. Annalen, 268 (1984) 197-206
• The Hodge group of an abelian variety

Proc. Amer. Math. Soc. 104 (1) (1988) 61-68
• Algebraic cycles on abelian varieties

Duke Math J. 50 (1983) 487-504
• Odd values of the Ramanujan $\tau$ Function

with Murty, Ram M., and Shorey, T.N.
Bulletin Math. Soc. France 115 (1987) 391-395
• Modular forms and the Chebotarev density theorem

with Murty, Ram M., and Saradha, N.
Amer. Journal of Math. 110 (1988) 253-281
• On the enumeration of finite groups

with Murty, Ram M., and Erdos, P.
J. Number Theory 25 (1987) 360-378
• The number of groups of a given order

with Murty, Ram M.
J. Number Theory 18 (1984) 178-191
• The Euclidean algorithm for $S$-integers

with Murty, Ram M., and Gupta, R.
CMS Conference Proceedings 7 (1987) 189-201
• Zeros and poles of Artin $L$-functions

with Foote, R.
Math. Proc. Camb. Phil. Soc. 105 (1989) 5-11
• A variant of the Bombieri Vinogradov theorem

with Murty, Ram M.
CMS Conference proceedings, 7 (1987) 243-272
• Explicit formulae and the Lang-Trotter conjecture

Rocky Mountain J. Math. 15 (2) (1985) 535-551