Notes On Generalized Dedekind Sums
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Notes On Generalized Dedekind Sums
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Author : Donald E. Knuth
language : en
Publisher:
Release Date : 1975
Notes On Generalized Dedekind Sums written by Donald E. Knuth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Combinatorial number theory categories.
Generalized Dedekind sums sigma(h, k, c) have proved to be useful in connection with the analysis of linear congruential random number generators. This paper introduces a simple algorithm for the calculation of generalized Dedekind sums using only integer arithmetic. A second algorithm, for calculating the value of c which maximizes or minimizes sigma(h, k, c) when h and k are given, is used to deduce optimal a priori bounds on sigma(h, k, c). Finally the reciprocity law for Dedekind sums is shown to be a consequence of a much more general reciprocity law.
Dedekind Sums
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Author : Hans Rademacher
language : en
Publisher: American Mathematical Soc.
Release Date : 1972-12-31
Dedekind Sums written by Hans Rademacher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-12-31 with MATHEMATICS categories.
These notes from Hans Rademacher's 1963 Hedrick Lectures have been gently polished and augmented by Emil Grosswald. While the topic itself is specialized, these sums are linked in diverse ways to many results in number theory, elliptical modular functions, and topology. The first main result is a surprising reciprocity law that is equivalent to the law of quadratic reciprocity.
An Axiomatic Approach To Generalized Dedekind Sums
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Author : Shinji Fukuhara
language : en
Publisher:
Release Date : 1995
An Axiomatic Approach To Generalized Dedekind Sums written by Shinji Fukuhara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Dedekind sums categories.
A Study Of Dedekind Sums And Their Generalization
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Author : Tom Mike Apostol
language : en
Publisher:
Release Date : 1948
A Study Of Dedekind Sums And Their Generalization written by Tom Mike Apostol and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with categories.
Generalized Dedekind Rademacher Sums
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Author : James Richard Krabill
language : en
Publisher:
Release Date : 1971
Generalized Dedekind Rademacher Sums written by James Richard Krabill and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Arithmetic functions categories.
Generalized Dedekind Bernoulli Sums
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Author : Anastasia Chavez
language : en
Publisher:
Release Date : 2010
Generalized Dedekind Bernoulli Sums written by Anastasia Chavez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Unusual Applications Of Number Theory
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Author : Melvyn Bernard Nathanson
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Unusual Applications Of Number Theory written by Melvyn Bernard Nathanson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Literary Criticism categories.
This volume contains the proceedings of the workshop held at the DIMACS Center of Rutgers University (Piscataway, NJ) on Unusual Applications of Number Theory. Standard applications of number theory are to computer science and cryptology. In this volume, well-known number theorist, Melvyn B. Nathanson, gathers articles from the workshop on other, less standard applications in number theory, as well as topics in number theory with potential applications in science and engineering. The material is suitable for graduate students and researchers interested in number theory and its applications.
Journal Of Research Of The National Bureau Of Standards
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1970
Journal Of Research Of The National Bureau Of Standards written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematical physics categories.
Journal Of Research Of The National Bureau Of Standards
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Author :
language : en
Publisher:
Release Date : 1970
Journal Of Research Of The National Bureau Of Standards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematical physics categories.
Computing The Continuous Discretely
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Author : Matthias Beck
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-19
Computing The Continuous Discretely written by Matthias Beck 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 2007-11-19 with Mathematics categories.
This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.