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Automorphic Representations and $$L$$-functions
 Tata Institute of Fundamental Research 2013; 550 pp; hardcover ISBN-10: 93-80250-49-5 ISBN-13: 978-93-80250-49-6 List Price: US$150 Member Price: US$120 Order Code: TIFR/18 This volume contains the proceedings of the International Colloquium on Representations and $$L$$-functions organized by the Tata Institute of Fundamental Research in January 2012, one of a series of colloquia that began in 1956. It covers a wide spectrum of mathematics, including classifications of representations, arithmeticity, the average size of the 2-Selmer group of Jacobians for certain hyperelliptic curves, certain Kuznetsov formula for symmetry types of families of $$L$$-functions, sub-convexity bounds in the level aspect, Linnik's ergodic method, beyond endoscopy, and harmonic analysis for the relative trace formula. This volume contains refereed articles by leading experts in these fields and includes original results as well as expository materials in these areas. A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka. Readership Graduate students and research mathematicians interested in number theory. Table of Contents J. Arthur -- The endoscopic classification of representations M. Bhargava and B. D. Gross -- The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point P. Cho and H. Kim -- Weil's theorem on rational points over finite fields and Artin $$L$$-functions W. T. Gan and A. Raghuram -- Arithmeticity for periods of automorphic forms E. Ghate and N. Kumar -- Control theorems for ordinary 2-adic families of modular forms D. Goldfeld and A. Kontororich -- On the $$GL(3)$$ Kuznetsov formula with applications to symmetry types of families of $$L$$-functions R. Holowinsky and R. Munshi -- Level aspect sub-convexity for Rankin-Selberg $$L$$-functions E. Lapid -- On the Harish-Chandra Schwartz space of $$G(F)\backslash G(A)$$ S. T. Lee and C. Zhu -- Degenerate principal series of metaplectic groups and Howe correspondence P. Michel, J. Ellenberg, and A. Venkatesh -- Linnik's ergodic method and distribution of integer points on spheres R. Murty -- The Fibonacci Zeta-function D. Ramakrishnan -- Decomposition and signs of $$l$$-adic representations attached to algebraic automorphic forms on $$GL(4)$$ D. Rohrlich -- Self-dual Artin representations A. Saha -- Determination of modular forms by fundamental Fourier coefficients Y. Sakellaridis -- Beyond endoscopy for the relative trace formula I : Local theory M. Tadic -- On interactions between harmonic analysis and the theory of automorphic forms E. Urban -- On the rank of Selmer groups of elliptic curves over $$Q$$ W. Zhang -- Harmonic analysis for relative trace formula