Number theory

In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry.

The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane.

This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series.

This book is a general introduction to Higher AlgebraicK-groups of rings and algebraic varieties, which were firstdefined by Quillen at the beginning of the 70's.

This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.

The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "e;Diophantine approximation onabelian varieties"e;, Ann.

The number field sieve is an algorithm for finding the prime factors of large integers.

This book is the first volume of proceedings from the joint conference X International Symposium "e;Quantum Theory and Symmetries"e; (QTS-X) and XII International Workshop "e;Lie Theory and Its Applications in Physics"e; (LT-XII), held on 19-25 June 2017 in Varna, Bulgaria.

The New York Number Theory Seminar was organized in 1982 to provide a forum for the presentation and discussion of recent advances in higher arithmetic and its applications.

With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right.

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.

This book is a great treasure for everyone who enjoys the beauty of the fascinating world of recreational mathematics.

The author had initiated a revision and translation of"e;Classical Diophantine Equations"e; prior to his death.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic.

These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of C resp.

This book continues the applications of mathematics, more specifically of theta, eta, and zeta functions, and modular forms, to various areas of theoretical physics.

This proceedings volume, the sixth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 20th and 21st annual workshops, held in New York in 2022 (virtual) and 2023 (hybrid) respectively.

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It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years.

This book provides an accessible introduction to the theory of L-functions, emphasising their central role in number theory and their direct applications to key results.

1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:.

This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster.

This volume records and disseminates selected papers from the Stinson66 conference, including surveys, prospectives, and papers presenting original and current research.

Eugene Charles Catalan made his famous conjecture - that 8 and 9 are the only two consecutive perfect powers of natural numbers - in 1844 in a letter to the editor of Crelle's mathematical journal.

This book is intended as a text for a course on cryptography with emphasis on algebraic methods.

These notes give an account of recent work in harmonic analysis dealing with the analytical foundations of A.

The aim of this book is to present an exposition of the theory of alge- braic numbers, excluding class-field theory and its consequences.

These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q).

This book gathers carefully chosen selection tests proposed to IMO (International Mathematical Olympiad) teams across many countries.

Abelian varieties are special examples of projectivevarieties.

The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur.

Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back- ground or maturity from the reader, and which can be read and understood with no extra assistance.

Number theory as studied by the logician is the subject matter of the book.

This textbook provides an undergraduate introduction to Galois theory and its most notable applications.

Inspired by the classic Recreations in the Theory of Numbers-The Queen of Mathematics Entertains by Albert H.

This volume contains the notes originally made by Kenkichi Iwasawa in his own handwriting for his lecture course at Princeton University in 1964.

This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup.

This book collects original research papers and survey articles presented at two conferences on the same theme: the International Conference on Class Groups of Number Fields and Related Topics, held at Kerala School of Mathematics, Kozhikode, Kerala, India, from 21-24 October 2021 and then from 21-24 November 2022.