Henryk Iwaniec - Böcker

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques.The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercises in each section serve a dual purpose, with some intended to improve the reader's understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much necessary information about them included in two survey chapters.

Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style.The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of L2 functionson the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues.Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.

This volume contains the proceedings of IDPEIS-22: Isomonodromic Deformations, Painleve Equations, and Integrable Systems, held virtually June 27-July 1, 2022, hosted by Columbia University, and AGMPS-22: Algebraic Geometry, Mathematical Physics, and Solitons, held October 7-9, 2022, at Columbia University, New York, NY. This volume is dedicated to the legacy of Igor Krichever, and the papers in it are closely connected to the main themes of Igor's research interests. The range of topics in this volume is very broad. The paper by Bobenko, Bobenko, and Suris generalizes Krichever's approach to algebro-geometric integrability to the dimer models. The paper by Rohrle and Zakharov considers a tropical version of classical algebro-geometric objects such as the Prym variety. The papers by Grekov and Nekrasov and by Felder, Smirnov, Tarasov, and Varchenko study quantum integrable systems from the point of view of 3D mirror symmetry and gauge theories. The paper by Etingof and Varchenko studies properties of certain families of flat connections, and the paper by Yamada describes a Lax form of a quantum $q$-Painleve equation. The paper by Cherednik belongs to the area of combinatorial probability and the paper by Braverman and Kazhdan to the geometric Langlands program. The two remaining papers are in the area of applied mathematics. The paper by de Leon, Frauendiener, and Klein considers the computational approach to the Schotky problem. The paper by Blackstone, Gassot, and Miller studies soliton ensembles for the Benjamin-Ono equation.