Geometry, Algebra, Number Theory, and Their Information Technology Applications: Toronto, Canada, June, 2016, and Kozhikode, India, August, 2016

Description

This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functionsArithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varietiesThe emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology. Front Matter ....Pages i-vi Overview of the Work of Kumar Murty (Amir Akbary, Sanoli Gun, M. Ram Murty)....Pages 1-18 On the Average Value of a Function of the Residual Index (Amir Akbary, Adam Tyler Felix)....Pages 19-37 Applications of the Square Sieve to a Conjecture of Lang and Trotter for a Pair of Elliptic Curves Over the Rationals (S. Baier, Vijay M. Patankar)....Pages 39-57 R-Group and Multiplicity in Restriction for Unitary Principal Series of GSpin and Spin (Dubravka Ban, Kwangho Choiy, David Goldberg)....Pages 59-69 The 2-Class Tower of \(\mathbb {Q}(\sqrt{-5460})\) (Nigel Boston, Jiuya Wang)....Pages 71-80 On the Bad Reduction of Certain U(2, 1) Shimura Varieties (Ehud de Shalit, Eyal Z. Goren)....Pages 81-152 Density Modulo 1 of a Sequence Associated with a Multiplicative Function Evaluated at Polynomial Arguments (Jean-Marc Deshouillers, Mohammad Nasiri-Zare)....Pages 153-161 Uniqueness Results for a Class of L-Functions (Anup B. Dixit)....Pages 163-181 Quadratic Periods of Meromorphic Forms on Punctured Riemann Surfaces (Payman Eskandari)....Pages 183-205 On the Local Coefficients Matrix for Coverings of \(\mathrm{SL}_2\) (Fan Gao, Freydoon Shahidi, Dani Szpruch)....Pages 207-244 Eisenstein Series of Weight One, q-Averages of the 0-Logarithm and Periods of Elliptic Curves (Daniel R. Grayson, Dinakar Ramakrishnan)....Pages 245-266 On Zeros of Certain Cusp Forms of Integral Weight for Full Modular Group (Murugesan Manickam, E. M. Sandeep)....Pages 267-271 A Note on Burgess Bound (Ritabrata Munshi)....Pages 273-289 A Smooth Selberg Sieve and Applications (M. Ram Murty, Akshaa Vatwani)....Pages 291-315 Explicit Arithmetic on Abelian Varieties (V. Kumar Murty, Pramathanath Sastry)....Pages 317-374 Derived Categories of Moduli Spaces of Vector Bundles on Curves II (M. S. Narasimhan)....Pages 375-382 Representations of an Integer by Some Quaternary and Octonary Quadratic Forms (B. Ramakrishnan, Brundaban Sahu, Anup Kumar Singh)....Pages 383-409 A Topological Realization of the Congruence Subgroup Kernel (John Scherk)....Pages 411-417 Fine Selmer Groups and Isogeny Invariance (R. Sujatha, M. Witte)....Pages 419-444 Distribution of a Subset of Non-residues Modulo p (R. Thangadurai, Veekesh Kumar)....Pages 445-459 On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors (Guangwu Xu)....Pages 461-476 Endomorphism Algebras of Abelian Varieties with Special Reference to Superelliptic Jacobians (Yuri G. Zarhin)....Pages 477-528