Tata Institute of Fundamental Research 2001; 251 pp; softcover ISBN10: 8173194211 ISBN13: 9788173194214 List Price: US$32 Member Price: US$25.60 Order Code: TIFR/4
 This collection of papers is based on lectures delivered at the Tata Institute of Fundamental Research (TIFR) as part of a special year on arithmetic groups, \(L\)functions and automorphic forms. The volume opens with an article by Cogdell and PiatetskiShapiro on Converse Theorems for \(GL_n\) and applications to liftings. It ends with some remarks on the Riemann Hypothesis by Ram Murty. Other talks cover topics such as Hecke theory for Jacobi forms, restriction maps and \(L\)values, congruences for Hilbert modular forms, Whittaker models for \(p\)adic \(GL(4)\), the Seigel formula, newforms for the Maaß Spezialchar, an algebraic Chebotarev density theorem, a converse theorem for Dirichlet series with poles, Kirillov theory for \(GL_2(\mathcal{D})\), and the \(L^2\) Euler characteristic of arithmetic quotients. The present volume is the latest in the Tata Institute's tradition of recognized contributions to number theory. 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  Cogdell and PiatetskiShapiro  Converse theorems for \(\mathrm{GL}_n\) and their application to liftings
 E. Ghate  Congruences between basechange and nonbasechange Hilbert modular forms
 C. Khare  Restriction maps and Lvalues
 M. Manickam  On Hecke theory for Jacobi forms
 A. N. Nair  The \(L^2\) Euler characteristic of arithmetic quotients
 D. Prasad  The space of degenerate Whittaker models for \(\mathrm{GL}(4)\) over padic fields
 S. Raghavan  The Seigel formula and beyond
 R. Raghunathan  A converse theorem for Dirichlet series with poles
 A. Raghuram  Kirillov theory for \(\mathrm{GL}_2(\mathcal{D})\)
 C. S. Rajan  An algebraic Chebotarev density theorem
 B. Ramakrishnan  Theory of newforms for the Maaß Spezialschar
 M. R. Murty  Some remarks on the Riemann hypothesis
 D. Prasad and N. Sanat  On the restriction of cuspidal representations to unipotent elements
 W. Kohnen and J. Sengupta  Nonvanishing of symmetric square \(L\)functions of cusp forms inside the critical strip
 H. H. Kim and F. Shahidi  Symmetric cube for \(\mathrm{GL}_2\)
 D. S. Thakur  Lfunctions and modular forms in finite characteristic
 T. C. Vasudevan  Automorphic forms for Siegel and Jacobi modular groups
 T. N. Venkataramana  Restriction maps between cohomology of locally symmetric varieties
