Number Fields and Function Fields – Two Parallel Worlds

Number Fields and Function Fields – Two Parallel Worlds PDF

Author: Gerard van der Geer

Publisher: Birkhäuser

Published: 2008-11-01

Total Pages: 321

ISBN-13: 9780817671051

DOWNLOAD EBOOK →

Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections

Number Fields and Function Fields – Two Parallel Worlds

Number Fields and Function Fields – Two Parallel Worlds PDF

Author: Gerard B. M. van der Geer

Publisher: Springer Science & Business Media

Published: 2006-11-24

Total Pages: 323

ISBN-13: 0817644474

DOWNLOAD EBOOK →

Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections

Arithmetic Geometry over Global Function Fields

Arithmetic Geometry over Global Function Fields PDF

Author: Gebhard Böckle

Publisher: Springer

Published: 2014-11-13

Total Pages: 350

ISBN-13: 3034808534

DOWNLOAD EBOOK →

This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.

From Arithmetic to Zeta-Functions

From Arithmetic to Zeta-Functions PDF

Author: Jürgen Sander

Publisher: Springer

Published: 2016-12-29

Total Pages: 552

ISBN-13: 3319282034

DOWNLOAD EBOOK →

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

Three Lectures on Commutative Algebra

Three Lectures on Commutative Algebra PDF

Author: Holger Brenner

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 202

ISBN-13: 0821844342

DOWNLOAD EBOOK →

These lectures provides detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications: tight closure and vector bundles; combinatorics and commutative algebra; constructive desingularization."

Casimir Force, Casimir Operators and the Riemann Hypothesis

Casimir Force, Casimir Operators and the Riemann Hypothesis PDF

Author: Gerrit van Dijk

Publisher: Walter de Gruyter

Published: 2010

Total Pages: 295

ISBN-13: 311022612X

DOWNLOAD EBOOK →

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Open Problems in Mathematics

Open Problems in Mathematics PDF

Author: John Forbes Nash, Jr.

Publisher: Springer

Published: 2016-07-05

Total Pages: 543

ISBN-13: 3319321625

DOWNLOAD EBOOK →

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Lanterna Rally - Theme by Grace Themes