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Lattice Points
This book is devoted to a special problem of number theory, that is the estimation of the number of lattice points in large closed domains of ordinary Euclidean spaces. Circle and sphere problems, Dirichlet's divisor problem, the distribution of powerful numbers, and finite Abelian groups are also investigated. The object of this book is to acquaint the reader with the fundamental results and methods, so that follow up with the original papers is possible.
Unsolved Problems in Number Theory
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
A Panoramic View of Riemannian Geometry
This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS
Reviews in Number Theory, 1984-96
These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.
The Genesis of General Relativity
This four-volume work represents the most comprehensive documentation and study of the creation of general relativity. Einstein’s 1912 Zurich notebook is published for the first time in facsimile and transcript and commented on by today’s major historians of science. Additional sources from Einstein and others, who from the late 19th to the early 20th century contributed to this monumental development, are presented here in translation for the first time. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity.
A Panorama of Discrepancy Theory
This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.
Analytische Funktionen in der Zahlentheorie
Im Mittelpunkt des Buches steht die Behandlung von Funktionalgleichungen analytischer Funktionen, die für die Anwendungen in der Zahlentheorie von Interesse sind. Ausgehend vom Gedankenkreis des quadratischen Reziprozitätsgesetzes werden die analytischen Grundlagen durch die Jacobischen Thetafunktionen und die Dedekindsche Etafunktion gelegt und ihre Beziehungen zu den Gaußschen und Dedekindschen Summen erörtert. Anschließend werden Verallgemeinerungen dieser Funktionen bezüglich höherer arithmetischer Probleme besprochen. Schließlich werden analytische Funktionen über konvexen Körpern betrachtet und Abschätzungen von Gitterpunktanzahlen in konvexen Körpern vorgenommen.
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