Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series.

The central theme of the exposition...

Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository articles and new developments extending from Yuri I. Manin s outstanding contributions to algebra, algebraic geometry, number theory, algorithmic complexity, noncommutative geometry and mathematical physics.

Among Manin s numerous achievements are the proof of the functional analogue of the Mordell conjecture, the theory of Gauss--Manin connection, the proof with V. Iskovskikh of the nonrationality of smooth quartic threefolds, the theory of $p$-adic automorphic functions, and the...

This book is devoted to the study of rational and integral points on higher- dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em- phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con- structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and...