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Number Theory in Function Fields, Michael Rosen


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Автор: Michael Rosen
Название:  Number Theory in Function Fields
ISBN: 9781441929549
Издательство: Springer
Классификация:


ISBN-10: 1441929541
Обложка/Формат: Paperback
Страницы: 358
Вес: 0.53 кг.
Дата издания: 03.12.2010
Серия: Graduate Texts in Mathematics
Язык: English
Издание: Softcover reprint of
Иллюстрации: Black & white illustrations
Размер: 234 x 156 x 20
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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, Wilsons theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlets 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.


Spectral Theory of the Riemann Zeta-Function

Автор: Motohashi
Название: Spectral Theory of the Riemann Zeta-Function
ISBN: 0521058074 ISBN-13(EAN): 9780521058070
Издательство: Cambridge Academ
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Цена: 8554.00 р.
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Описание: Professor Motohashi shows that the Riemann zeta function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the function itself.

The Riemann Hypothesis for Function Fields

Автор: Frankenhuijsen
Название: The Riemann Hypothesis for Function Fields
ISBN: 1107685311 ISBN-13(EAN): 9781107685314
Издательство: Cambridge Academ
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Цена: 6019.00 р.
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Описание: A description of how non-commutative geometry could provide a means to attack the Riemann Hypothesis, one of the most important unsolved problems in mathematics. The book will be of interest to graduate students in analytic and algebraic number theory, and provides a strong foundation for further research in this area.

Analytic Function Theory of Several Variables

Автор: Noguchi
Название: Analytic Function Theory of Several Variables
ISBN: 9811002894 ISBN-13(EAN): 9789811002892
Издательство: Springer
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Цена: 8384.00 р.
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Описание: This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later.The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap.

Operator Theory, Function Spaces, and Applications

Автор: Eisner
Название: Operator Theory, Function Spaces, and Applications
ISBN: 3319313819 ISBN-13(EAN): 9783319313818
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of Damir Arov and to the sixty-fifth birthday of Leiba Rodman, both leading figures in the area of operator theory and its applications, in particular, to systems theory.

The Riemann Hypothesis for Function Fields

Автор: Frankenhuijsen
Название: The Riemann Hypothesis for Function Fields
ISBN: 1107047218 ISBN-13(EAN): 9781107047211
Издательство: Cambridge Academ
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Цена: 16790.00 р.
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Описание: A description of how non-commutative geometry could provide a means to attack the Riemann Hypothesis, one of the most important unsolved problems in mathematics. The book will be of interest to graduate students in analytic and algebraic number theory, and provides a strong foundation for further research in this area.

Number Theory and Related Fields

Автор: Jonathan M. Borwein; Igor Shparlinski; Wadim Zudil
Название: Number Theory and Related Fields
ISBN: 1493902172 ISBN-13(EAN): 9781493902170
Издательство: Springer
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Цена: 16769.00 р.
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Описание: "Number Theory and Related Fields" collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia.

The Theory of Algebraic Number Fields

Автор: David Hilbert; F. Lemmermeyer; I.T. Adamson; N. Sc
Название: The Theory of Algebraic Number Fields
ISBN: 3642083064 ISBN-13(EAN): 9783642083068
Издательство: Springer
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Цена: 12577.00 р.
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Описание: Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is- chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati- cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.

Number Theory and Related Fields

Автор: Jonathan M. Borwein; Igor Shparlinski; Wadim Zudil
Название: Number Theory and Related Fields
ISBN: 1461466415 ISBN-13(EAN): 9781461466413
Издательство: Springer
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Цена: 13974.00 р.
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Описание: "Number Theory and Related Fields" collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia.

Algebraic function fields and codes

Автор: Stichtenoth, Henning
Название: Algebraic function fields and codes
ISBN: 3642095569 ISBN-13(EAN): 9783642095566
Издательство: Springer
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Цена: 7685.00 р.
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Описание: This is an expanded edition of a popular textbook that provides a purely algebraic, self-contained and in-depth exposition of the theory of function fields. It contains numerous exercises, some fairly simple, some quite difficult.


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