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Cohomology of Arithmetic Groups, $$L$$-Functions and Automorphic Forms
 Tata Institute of Fundamental Research 2001; 251 pp; softcover ISBN-10: 81-7319-421-1 ISBN-13: 978-81-7319-421-4 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 Piatetski-Shapiro 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 Piatetski-Shapiro -- Converse theorems for $$\mathrm{GL}_n$$ and their application to liftings E. Ghate -- Congruences between base-change and non-base-change Hilbert modular forms C. Khare -- Restriction maps and L-values 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 p-adic 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 -- L-functions 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