Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt
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Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt
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Author : George E Andrews
language : en
Publisher: World Scientific
Release Date : 2024-08-19
Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt written by George E Andrews and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-19 with Mathematics categories.
This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.
Jacobsthal Sums
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Author : Bogdan Nica
language : en
Publisher: World Scientific
Release Date : 2025-05-27
Jacobsthal Sums written by Bogdan Nica and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-27 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.
Transcendence In Algebra Combinatorics Geometry And Number Theory
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Author : Alin Bostan
language : en
Publisher: Springer Nature
Release Date : 2021-11-02
Transcendence In Algebra Combinatorics Geometry And Number Theory written by Alin Bostan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Mathematics categories.
This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1994
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Number Theory In The Spirit Of Ramanujan
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Number Theory In The Spirit Of Ramanujan written by Bruce C. Berndt 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 2006 with Mathematics categories.
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.
The Legacy Of Alladi Ramakrishnan In The Mathematical Sciences
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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-26
The Legacy Of Alladi Ramakrishnan In The Mathematical Sciences written by Krishnaswami Alladi 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 2010-08-26 with Mathematics categories.
Alladi Ramakrishnan (1923–2008) was an eminent scientist who had a wide range of research interests in theoretical and mathematical physics. Professor Ramakrishnan made signi?cant contributions to probability and statistics, elem- tary particle physics, cosmic rays and astrophysics, matrix theory, and the special theory of relativity. Ramakrishnan believedstrongly that in addition to doing fun- mental research, one must contribute to the advancementof the profession. Inspired by his visit to the Institute for Advanced Study in Princeton in 1957–1958, he returned to Madras and began the Theoretical Physics Seminar at his family home Ekamra Nivas. These seminars were ultimately responsible for the creation of MATSCIENCE, The Institute of Mathematical Sciences in 1962. This institute, of which he was the Director for its ?rst 21years, has grown steadily in size and stature, and is his monumental contribution to the profession. In a distinguished scienti?c life that has spanned more than ?ve decades, Professor Ramakrishnan has come into close contact with, and was in?uenced by, several eminent mathema- cians and physicists, and has moulded the careers of his several students and young researchers. This volume, which is a tribute to his great legacy, not only deals with his signi?cant contributions to research and the profession, but also contains a ?ne collection of research and survey papers by leading physicists and mathematicians that cover a broad range of areas in the mathematical sciences.
George E Andrews 80 Years Of Combinatory Analysis
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Author : Krishnaswami Alladi
language : en
Publisher: Birkhäuser
Release Date : 2022-02-11
George E Andrews 80 Years Of Combinatory Analysis written by Krishnaswami Alladi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-11 with Mathematics categories.
This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.
Topics And Methods In Q Series
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Author : James Mc Laughlin
language : en
Publisher: World Scientific
Release Date : 2017-09-22
Topics And Methods In Q Series written by James Mc Laughlin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-22 with Mathematics categories.
The book provides a comprehensive introduction to the many aspects of the subject of basic hypergeometric series. The book essentially assumes no prior knowledge but eventually provides a comprehensive introduction to many important topics. After developing a treatment of historically important topics such as the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, Ramanujan's 1-psi-1 summation formula, Bailey's 6-psi-6 summation formula and the Rogers-Fine identity, the book goes on to delve more deeply into important topics such as Bailey- and WP-Bailey pairs and chains, q-continued fractions, and mock theta functions. There are also chapters on other topics such as Lambert series and combinatorial proofs of basic hypergeometric identities.The book could serve as a textbook for the subject at the graduate level and as a textbook for a topic course at the undergraduate level (earlier chapters). It could also serve as a reference work for researchers in the area.
Notebooks Of Srinivasa Ramanujan
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Author : Srinivasa Ramanujan Aiyangar
language : en
Publisher:
Release Date : 1957
Notebooks Of Srinivasa Ramanujan written by Srinivasa Ramanujan Aiyangar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with categories.
Number Theory And Discrete Mathematics
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Author : A.K. Agarwal
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Number Theory And Discrete Mathematics written by A.K. Agarwal and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
To mark the World Mathematical Year 2000 an International Conference on Number Theory and Discrete Mathematics in honour of the legendary Indian Mathematician Srinivasa Ramanuj~ was held at the centre for Advanced study in Mathematics, Panjab University, Chandigarh, India during October 2-6, 2000. This volume contains the proceedings of that conference. In all there were 82 participants including 14 overseas participants from Austria, France, Hungary, Italy, Japan, Korea, Singapore and the USA. The conference was inaugurated by Prof. K. N. Pathak, Hon. Vice-Chancellor, Panjab University, Chandigarh on October 2, 2000. Prof. Bruce C. Berndt of the University of Illinois, Urbana Chaimpaign, USA delivered the key note address entitled "The Life, Notebooks and Mathematical Contributions of Srinivasa Ramanujan". He described Ramanujan--as one of this century's most influential Mathematicians. Quoting Mark K. ac, Prof. George E. Andrews of the Pennsylvania State University, USA, in his message for the conference, described Ramanujan as a "magical genius". During the 5-day deliberations invited speakers gave talks on various topics in number theory and discrete mathematics. We mention here a few of them just as a sampling: • M. Waldschmidt, in his article, provides a very nice introduction to the topic of multiple poly logarithms and their special values. • C.