Tata Institute of Fundamental Research 2013; 550 pp; hardcover ISBN10: 9380250495 ISBN13: 9789380250496 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 2Selmer group of Jacobians for certain hyperelliptic curves, certain Kuznetsov formula for symmetry types of families of \(L\)functions, subconvexity 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 2Selmer 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 2adic 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 subconvexity for RankinSelberg \(L\)functions
 E. Lapid  On the HarishChandra 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 Zetafunction
 D. Ramakrishnan  Decomposition and signs of \(l\)adic representations attached to algebraic automorphic forms on \(GL(4)\)
 D. Rohrlich  Selfdual 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
