Libros de Matemáticas, página 47 de 472

ANALYTIC CAPACITY AND MEASURE

Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

This invaluable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable ("elementary") and complex variable ("analytic") methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.

El libro presenta, con gran detalle, las nociones y resultados básicos sobre anillos y cuerpos conmutativos, poniendo especial énfasis en la resolución de algunas cuestiones fundamentales acerca de polinomios en una y varias variables. Lo anterior incluye ecuaciones diofánticas, polinomios simétricos, raíces reales, los rudimentos de la teoría de Galois en característica cero y cuerpos finitos.

El concepto de anillo de multiplicación nos permite estudiar bajo el mismo prisma dominios Dedekind, anillos primarios especiales y anillos regulares von Neumann. La obra no sólo recoge y organiza el material existente sino que cuenta con aportaciones originales de los autores publicadas en distintos articulos de investigacion o hasta entonces ineditas. En el trabajo se muestra que los resultados e ideas se pueden aplicar a campos tan diversos como algebra conmutativa, geometria algebraica, teoria de categorias, teoria de anillos, topologias de Gabriel, etc.