Topics In Arithmetical Functions
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Arithmetical Functions
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Author : Komaravolu Chandrasekharan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetical Functions written by Komaravolu Chandrasekharan 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.
The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. My Introduction to Analytic Number Theory has appeared in the meanwhile, and this book may be looked upon as a sequel. It presupposes only a modicum of acquaintance with analysis and number theory. The arithmetical functions considered here are those associated with the distribution of prime numbers, as well as the partition function and the divisor function. Some of the problems posed by their asymptotic behaviour form the theme. They afford a glimpse of the variety of analytical methods used in the theory, and of the variety of problems that await solution. I owe a debt of gratitude to Professor Carl Ludwig Siegel, who has read the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the manuscript and correcting the proofs. K. Chandrasekharan July 1970 Contents Chapter I The prime number theorem and Selberg's method § 1. Selberg's fonnula . . . . . . 1 § 2. A variant of Selberg's formula 6 12 § 3. Wirsing's inequality . . . . . 17 § 4. The prime number theorem. .
Topics In Multiplicative Number Theory
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Author : Hugh L. Montgomery
language : en
Publisher: Springer
Release Date : 2006-11-15
Topics In Multiplicative Number Theory written by Hugh L. Montgomery and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
These notes are designed to present a survey of the present state of knowledge concerning those subjects touched upon in the last fifty pages of Davenport's Multiplicative Number Theory .
Advanced Topics In The Arithmetic Of Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Advanced Topics In The Arithmetic Of Elliptic Curves written by Joseph H. Silverman 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 2013-12-01 with Mathematics categories.
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
Topics From The Theory Of Numbers
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Author : Emil Grosswald
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-23
Topics From The Theory Of Numbers written by Emil Grosswald 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 2010-02-23 with Mathematics categories.
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: (1) divisibility, (2) congruences, (3) the Riemann zeta function, (4) Diophantine equations and Fermat’s conjecture, (5) the theory of partitions. Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike.
Arithmetic Tales
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Author : Olivier Bordellès
language : en
Publisher: Springer
Release Date : 2020-11-27
Arithmetic Tales written by Olivier Bordellès and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-27 with Mathematics categories.
This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
An Introduction To The Theory Of Numbers
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Author : Leo Moser
language : en
Publisher: The Trillia Group
Release Date : 2004
An Introduction To The Theory Of Numbers written by Leo Moser and has been published by The Trillia Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
"This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description
Arithmetical Functions
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Author : Wolfgang Schwarz
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-10
Arithmetical Functions written by Wolfgang Schwarz 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 1994-03-10 with Mathematics categories.
Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis.
Topics In The Theory Of Algebraic Function Fields
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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.
Classical Theory Of Arithmetic Functions
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Author : R Sivaramakrishnan
language : en
Publisher: Routledge
Release Date : 2018-10-03
Classical Theory Of Arithmetic Functions written by R Sivaramakrishnan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
Basic Structures Of Function Field Arithmetic
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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