The Riemann Hypothesis For Function Fields

DOWNLOAD

Download The Riemann Hypothesis For Function Fields PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Riemann Hypothesis For Function Fields book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

The Riemann Hypothesis For Function Fields

DOWNLOAD
Author : Machiel van Frankenhuijsen
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-09

The Riemann Hypothesis For Function Fields written by Machiel van Frankenhuijsen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.

This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area.

Number Theory In Function Fields

DOWNLOAD
Author : Michael Rosen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Number Theory In Function Fields written by Michael Rosen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.

Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con sidering finite algebraic extensions K of Q, which are called algebraic num ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K.

The Riemann Hypothesis In Characteristic P In Historical Perspective

DOWNLOAD
Author : Peter Roquette
language : en
Publisher: Springer
Release Date : 2018-09-28

The Riemann Hypothesis In Characteristic P In Historical Perspective written by Peter Roquette and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-28 with Mathematics categories.

This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.

The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field

DOWNLOAD
Author : Helmut Hasse
language : en
Publisher:
Release Date : 1968

The Riemann Hypothesis In Algebraic Function Fields Over A Finite Constants Field written by Helmut Hasse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Algebraic fields categories.

Topics In The Theory Of Algebraic Function Fields

DOWNLOAD
Author : Gabriel Daniel Villa Salvador
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-10

Topics In The Theory Of Algebraic Function Fields written by Gabriel Daniel Villa Salvador and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-10 with Mathematics categories.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

Number Fields And Function Fields Two Parallel Worlds

DOWNLOAD
Author : Gerard B. M. van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-24

Number Fields And Function Fields Two Parallel Worlds written by Gerard B. M. van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-24 with Mathematics categories.

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

Field Arithmetic

DOWNLOAD
Author : Michael D. Fried
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-29

Field Arithmetic written by Michael D. Fried and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-29 with Mathematics categories.

Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?

Function Field Arithmetic

DOWNLOAD
Author : Dinesh S. Thakur
language : en
Publisher: World Scientific
Release Date : 2004

Function Field Arithmetic written by Dinesh S. Thakur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This book provides an exposition of function field arithmetic withemphasis on recent developments concerning Drinfeld modules, thearithmetic of special values of transcendental functions (such as zetaand gamma functions and their interpolations), diophantineapproximation and related interesting open problems.

Basic Structures Of Function Field Arithmetic

DOWNLOAD
Author : David Goss
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Basic Structures Of Function Field Arithmetic written by David Goss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062

Arithmetic Geometry Over Global Function Fields

DOWNLOAD
Author : Gebhard Böckle
language : en
Publisher: Springer
Release Date : 2014-11-13

Arithmetic Geometry Over Global Function Fields written by Gebhard Böckle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Mathematics categories.

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.