"In the spirit of The Book of the One Thousand and One Nights, the authors offer 1001 problems in number theory in a way that entices the reader to immediately attack the next problem. Whether a novice of an experienced mathematician, anyone fascinated by numbers will find a gre…
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"In the spirit of The Book of the One Thousand and One Nights, the authors offer 1001 problems in number theory in a way that entices the reader to immediately attack the next problem. Whether a novice of an experienced mathematician, anyone fascinated by numbers will find a gre…
An anthology of articles designed to supplement a first course in number theory.
"This book is devoted to Diophantine equations where the solutions are taken from an integral domain of characteristic 0 that is finitely generated over Z, that is a domain of the shape Z[z1; : : : ; zr] with quotient field of characteristic 0, where the generators z1; : : : ; z…
"This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography. In Mathematics, a Mersenne number (named after Mari…
Discloses a variety of details about numbers like the year 1776 and discusses prime numbers and number patterns, and exposes revelatory properties of numbers. Also provides games and gambling with dice and playing cards along with mathematical puzzles.
"Robert Langlands' contributions to modern number theory, which is generally referred to as the "Langlands Program," has been visionary and ground breaking. The present volume is intended as homage to his early work in which the seeds of the program were planted. This volume cov…
"This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this trul…
"The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is …
"The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell con…
"A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p -adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and e…
Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been select…
A robust implementation for solving the S-unit equation and several application (C. Rasmussen) -- Computing classical modular forms for arbitrary congruence subgroups (E. Assaf) -- Square root time Coleman integration on superelliptic curves (A. Best) -- Computing classical modu…
