Publications
PAPERS
1) On the structure of locally potentially equivalent Galois representations (with C. S. Rajan), Journal of Number Theory, (2020), https://doi.org/10.1016/j.jnt.2020.05.020 21 pages
2) Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals, Proceedings of the 2016 conferences in honour of V. Kumar Murty’s sixtieth birthday held at Toronto, Canada (June 2016) and Kozhikode, India (August 2016), volume titled “Geometry, Algebra, Number Theory, and Their Information Technology Applications” in “Springer Proceedings in Mathematics and Statistics” series, Volume 251, September 2018, pages 39 -- 57
3) Distinguishing Galois representations by their normalized traces (with C. S. Rajan), Journal of Number Theory, Vol. 178, April 2017, pages 118–125
4) Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves (With Manisha Kulkarni and C. S. Rajan),
Journal of Number Theory, Vol. 164, July 2016, pages 87–102
5) Tate cycles on Abelian varieties with complex multiplication (with V. Kumar Murty), Canad. J. Math., Vol. 67 (1), 2015, http://dx.doi.org/10.4153/CJM-2014-001-2, pages 198-213
6) Using Elimination Theory to construct Rigid Matrices (with Abhinav. Kumar, Satya Lokam, J. Sarma), Computational Complexity, April 2013, 33 pp
7) Locally potentially equivalent Galois representations (with C. S. Rajan), J. Ramanujan Math. Soc. 27, No. 1 (2012), http://jrms.ramanujanmathsociety.org/archieves/v27-1.html, 77-90 Errata to this paper (in response to an error pointed out by Professor J.-P. Serre)
8) Splitting of Abelian Varieties (with V. Kumar Murty), International Mathematical Research Notices, 2008, No. 12, Art. ID rnn033, https://doi.org/10.1093/imrn/rnn033, 27 pp
9) Software integrity checking expressions (ICEs) for robust tamper detection (with M. Jakubowski, P. Naldurg, R. Venkatesan), Proceedings of the 9th
International workshop on Information Hiding 2007, Lec. Notes Comp. Sci. No. 4567 (2007), 96-111
10) Efficient algorithm for the arithmetic on the hyperelliptic Jacobians of genus 3 (with C. Guyot, K. Kaveh), Journal of Ramanujan Mathematical Society, 19 (2004),
No. 2, 119-159
Other
11) Two evenings with B. H. Gross (with Sneha V. Patankar), Interview with Professor B. H. Gross, Asia Pacific Mathematics Newsletter,
Vol. 3 , Issue 3, July 2013, 26--31 (http://www.asiapacific-mathnews.com/03/0303/0026_0031)
THESIS
1) DOCTORAL THESIS: Splitting of Abelian Varieties, University of Toronto (November 2005)
2) MASTER'S THESIS: Exposition of Tate's thesis and exposition of Chebotarev density theorem, Tata Institute of Fundamental Research, Mumbai and University of Bombay, Mumbai
PAPERS
1) On the structure of locally potentially equivalent Galois representations (with C. S. Rajan), Journal of Number Theory, (2020), https://doi.org/10.1016/j.jnt.2020.05.020 21 pages
2) Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals, Proceedings of the 2016 conferences in honour of V. Kumar Murty’s sixtieth birthday held at Toronto, Canada (June 2016) and Kozhikode, India (August 2016), volume titled “Geometry, Algebra, Number Theory, and Their Information Technology Applications” in “Springer Proceedings in Mathematics and Statistics” series, Volume 251, September 2018, pages 39 -- 57
3) Distinguishing Galois representations by their normalized traces (with C. S. Rajan), Journal of Number Theory, Vol. 178, April 2017, pages 118–125
4) Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves (With Manisha Kulkarni and C. S. Rajan),
Journal of Number Theory, Vol. 164, July 2016, pages 87–102
5) Tate cycles on Abelian varieties with complex multiplication (with V. Kumar Murty), Canad. J. Math., Vol. 67 (1), 2015, http://dx.doi.org/10.4153/CJM-2014-001-2, pages 198-213
6) Using Elimination Theory to construct Rigid Matrices (with Abhinav. Kumar, Satya Lokam, J. Sarma), Computational Complexity, April 2013, 33 pp
7) Locally potentially equivalent Galois representations (with C. S. Rajan), J. Ramanujan Math. Soc. 27, No. 1 (2012), http://jrms.ramanujanmathsociety.org/archieves/v27-1.html, 77-90 Errata to this paper (in response to an error pointed out by Professor J.-P. Serre)
8) Splitting of Abelian Varieties (with V. Kumar Murty), International Mathematical Research Notices, 2008, No. 12, Art. ID rnn033, https://doi.org/10.1093/imrn/rnn033, 27 pp
9) Software integrity checking expressions (ICEs) for robust tamper detection (with M. Jakubowski, P. Naldurg, R. Venkatesan), Proceedings of the 9th
International workshop on Information Hiding 2007, Lec. Notes Comp. Sci. No. 4567 (2007), 96-111
10) Efficient algorithm for the arithmetic on the hyperelliptic Jacobians of genus 3 (with C. Guyot, K. Kaveh), Journal of Ramanujan Mathematical Society, 19 (2004),
No. 2, 119-159
Other
11) Two evenings with B. H. Gross (with Sneha V. Patankar), Interview with Professor B. H. Gross, Asia Pacific Mathematics Newsletter,
Vol. 3 , Issue 3, July 2013, 26--31 (http://www.asiapacific-mathnews.com/03/0303/0026_0031)
THESIS
1) DOCTORAL THESIS: Splitting of Abelian Varieties, University of Toronto (November 2005)
2) MASTER'S THESIS: Exposition of Tate's thesis and exposition of Chebotarev density theorem, Tata Institute of Fundamental Research, Mumbai and University of Bombay, Mumbai