Jacobsthal Sums

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Teorija Isel Matemati Eskij Analiz I Ich Prilo Enija

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Author : Ivan Matveevich Vinogradov
language : en
Publisher: American Mathematical Soc.
Release Date : 1979

Teorija Isel Matemati Eskij Analiz I Ich Prilo Enija written by Ivan Matveevich Vinogradov 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 1979 with Mathematics categories.

"This collection of paper is dedicated to Academician Ivan Matveevic̆ Vinogradov on his eighty-fifth birthday. It consists of original work on various parts of number theory, analysis, and also their applications." Title page verso.

Jacobsthal Sums

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Author : Bogdan Nica
language : en
Publisher:
Release Date : 2025-06-06

Jacobsthal Sums written by Bogdan Nica and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-06 with Mathematics categories.

The focus of this monograph is on the Jacobsthal sums of the title. These are quadratic character sums with polynomial arguments of a certain simple form. In addition to studying Jacobsthal sums on their own, the monograph explores their role in several topics of number-theoretical interest. A prominent theme is their use in counting solutions to equations over prime fields. Another aim is to construct representations of primes as sums of squares using Jacobsthal sums. Finally, Jacobsthal sums are applied to evaluate other quadratic character sums with polynomial arguments. This text is self-contained, with minimal technical prerequisites. We have strived for an engaging exposition, incorporating numerous examples and applications, carefully selected exercises, and historical notes and perspectives. Complete solutions to all exercises are provided. This monograph should be of interest to researchers studying character sums or counting solutions to equations over finite fields, as well as to graduate students and advanced undergraduates interested in these topics.

Finite Fields

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Author : Rudolf Lidl
language : en
Publisher: Cambridge University Press
Release Date : 1997

Finite Fields written by Rudolf Lidl 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 1997 with Mathematics categories.

This book is devoted entirely to the theory of finite fields.

Reciprocity Laws

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Author : Franz Lemmermeyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Reciprocity Laws written by Franz Lemmermeyer 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 2013-03-14 with Mathematics categories.

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

Handbook Of Finite Fields

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Author : Gary L. Mullen
language : en
Publisher: CRC Press
Release Date : 2013-06-17

Handbook Of Finite Fields written by Gary L. Mullen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Computers categories.

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Gauss And Jacobi Sums

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Author : Bruce C. Berndt
language : en
Publisher: Wiley-Interscience
Release Date : 1998-06

Gauss And Jacobi Sums written by Bruce C. Berndt and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06 with Mathematics categories.

Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy.

Class Groups Of Number Fields And Related Topics

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Author : Kalyan Chakraborty
language : en
Publisher: Springer Nature
Release Date : 2020-01-17

Class Groups Of Number Fields And Related Topics written by Kalyan Chakraborty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-17 with Mathematics categories.

This book gathers original research papers and survey articles presented at the “International Conference on Class Groups of Number Fields and Related Topics,” held at Harish-Chandra Research Institute, Allahabad, India, on September 4–7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer–Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.

Sequences And Their Applications Seta 2010

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Author : Claude Carlet
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09

Sequences And Their Applications Seta 2010 written by Claude Carlet 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 2010-09 with Business & Economics categories.

This volumecontainstherefereedproceedingsoftheSixth International Conf- ence on Sequences and Their Applications (SETA 2010), held in Paris, France, September 13-17, 2010. The previous ?ve conferences were held in Singapore (RepublicofSingapore),Bergen(Norway),Seoul(SouthKorea),Beijing(China) and Lexington (USA). Topics of SETA include: – Randomness of sequences – Correlation (periodic and aperiodic types) and combinatorial aspects of - quences (di?erence sets) – Sequences with applications in coding theory and cryptography – Sequences over ?nite ?elds/rings/function ?elds – Linear and nonlinear feedback shift register sequences – Sequences for radar distance ranging, synchronization, identi?cation, and hardware testing – Sequences for wireless communication – Pseudorandom sequence generators – Boolean and vectorial functions for sequences, coding and/or cryptography – Multidimensional sequences and their correlation properties – Linear and nonlinear complexity of sequences The Technical Program Committee of SETA 2010 refereed 56 submitted - pers. Each paper was reviewed by at least 2 referees (at least 3 when an author was a TPC member) and the TPC selected 33 papers to be presented at the conference. In addition, we had 4 invited papers, byRobert Calderbank(Prin- ton University, USA), James Massey (retired from ETH Zurich, Switzerland), Jong-Seon No (Seoul National University, South Korea) and Arne Winterhof ¨ (Osterreichische Akademie der Wissenschaften, Austria). TheCo-chairsoftheTPCwereClaudeCarlet(Universit´ eParis8,France)and Alexander Pott (Otto-von-Guericke-Universit¨ at, Magdeburg, Germany). They wish to thank the other members of the ProgramCommittee: Thierry P.

Fundamental Number Theory With Applications

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Author : Richard A. Mollin
language : en
Publisher: CRC Press
Release Date : 2008-02-21

Fundamental Number Theory With Applications written by Richard A. Mollin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-21 with Computers categories.

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in i

Number Theory

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Author : Krishnaswami Alladi
language : en
Publisher: Springer
Release Date : 2006-11-14

Number Theory written by Krishnaswami Alladi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.