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Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt). All of the surveys were outgrowths of featured talks given during the Special Year in Number Theory and Combinatorics at the University of Florida, Gainesville, 2004-2005, and describe major progress on a broad range of topics. This volume is intended for mathematicians and graduate students interested in number theory and related areas.
Mathematics. --- Functions of a Complex Variable. --- Special Functions. --- Number Theory. --- Functions of complex variables. --- Functions, special. --- Number theory. --- Mathématiques --- Fonctions d'une variable complexe --- Théorie des nombres --- Number theory --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Algebra. --- Number study --- Numbers, Theory of --- Special functions. --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Special functions
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This book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians in history whose lives and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life with the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. Also, among the articles are reviews of three important books on Ramanujan’s mathematics and life. In addition, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number π, his pathbreaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being. From the Foreword by George Andrews—one of the greatest experts on Ramanujan's work: “Alladi, who has worked in several areas of number theory and analysis, and who, as editor of the Ramanujan Journal, is uniquely qualified to write these historical sketches which provide an unusual and compelling view of Ramanujan.” ABOUT THE AUTHOR Krishnaswami Alladi is professor of mathematics at the University of Florida, where he was the department chairman during 1998–2008. He received his PhD from the University of California, Los Angeles, in 1978. His research area is number theory, where he has made notable contributions. In 1987, during the Ramanujan Centennial in India, he got the inspiration to launch The Ramanujan Journal (now published by Springer), devoted to all areas of mathematics influenced by Ramanujan. He annually writes articles about Ramanujan and his place in the world of mathematics, for journals and newspapers. He is presently editor-in-chief of The Ramanujan Journal, editor of the book series Developments in Mathematics (Springer), and associate editor of Notices of the American Mathematical Society.
Mathematics -- Popular works. --- Mathematics. --- Quadratic forms. --- Mathematicians --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematics - General --- History --- History. --- Ramanujan Aiyangar, Srinivasa, --- Ṣrīnivāsa-Rāmānuja Aiyaṅgār, --- Ramanujan, Srinivasa, --- Aiyangar, Srinivasa Ramanujan, --- Iyengar, Srinivasa Iyengar Ramanuja, --- Ramanuja Iyengar, Srinivasa Iyengar, --- Ramanudzhan Aĭengar, --- Ramanujan, S. --- Ramanujam, S. --- Number theory. --- Mathematics, general. --- Number Theory. --- History of Mathematical Sciences. --- Scientists --- Number study --- Numbers, Theory of --- Algebra --- Math --- Science --- Annals --- Auxiliary sciences of history --- India. --- Bharat --- Bhārata --- Government of India --- Ḣindiston Respublikasi --- Inde --- Indi --- Indien --- Indii͡ --- Indland --- Indo --- Republic of India --- Sāthāranarat ʻIndīa --- Yin-tu
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In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Forms, Quadratic --- Lattice theory --- Quadratic forms --- Mathematics. --- Special functions. --- Number theory. --- Combinatorics. --- Number Theory. --- Special Functions. --- Diophantine analysis --- Forms, Binary --- Number theory --- Functions, special. --- Special functions --- Mathematical analysis --- Combinatorics --- Algebra --- Number study --- Numbers, Theory of --- Forms, Quadratic. --- Automorphic forms. --- Forms (Mathematics)
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Matemàtics --- Història --- Ramanujan Aiyangar, Srinivasa, --- Índia --- Ciències socials --- Humanitats --- Ciències polítiques --- Conspiracions --- Cops d'Estat --- Cròniques --- Cronologia --- Demografia històrica --- Descobriments geogràfics --- Diplomàcia --- Escàndols --- Filosofia de la història --- Fonts històriques --- Història antiga --- Història constitucional --- Història contemporània --- Història de l'antropologia --- Història de l'art --- Història de l'urbanisme --- Història de la ciència --- Història de la civilització --- Història de la dona --- Història de la filosofia --- Història de la lingüística --- Història de la literatura --- Història de la psicologia --- Història de la tecnologia --- Història de la veterinària --- Història de les biblioteques --- Història del dret --- Història del llibre --- Història del transport --- Història eclesiàstica --- Història econòmica --- Història local --- Història medieval --- Història militar --- Història moderna --- Història pública --- Història social --- Història universal --- Historiografia --- Llocs històrics --- Migració de pobles --- Reis i sobirans --- Cinema històric --- Protohistòria --- Sociologia històrica --- Ciències auxiliars de la història --- Didàctica de la història --- Historiadores --- Historiadors --- Previsió --- Científics --- Dones matemàtiques --- Matemàtica --- Aiyangar, Srinivasa Ramanujan, --- Iyengar, Srinivasa Iyengar Ramanuja, --- Ramanujan, S. --- Ramanujam, S. --- Ramanujan, Srinivasa, --- Ramanuja Iyengar, Srinivasa Iyengar, --- Ramanujan Aiyangar, Srinivasa --- Bharat --- República de la India --- República de l'Índia --- Àsia del Sud --- Ajantha (Índia) --- Assam (Índia : Estat) --- Calcuta (Índia) --- Delhi (Índia) --- Kodagu (Índia : Regió) --- Goa (Índia : Estat) --- Jammu i Caixmir (Índia : Estat) --- Kerala (Índia : Estat) --- Madràs (Índia) --- Madhya Pradesh (Índia : Estat) --- Maharashtra (Índia : Estat) --- Orissa (Índia : Estat) --- Panjab (Índia : Estat) --- Rajasthan (Índia : Estat) --- Uttar Pradesh (Índia : Estat) --- Caixmir (Àsia : Regió) --- Mathematics. --- Math --- Science --- Brahmaputra (Àsia : Curs d'aigua)
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This book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians in history whose lives and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life with the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. Also, among the articles are reviews of three important books on Ramanujan’s mathematics and life. In addition, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number π, his pathbreaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being. From the Foreword by George Andrews—one of the greatest experts on Ramanujan's work: “Alladi, who has worked in several areas of number theory and analysis, and who, as editor of the Ramanujan Journal, is uniquely qualified to write these historical sketches which provide an unusual and compelling view of Ramanujan.” ABOUT THE AUTHOR Krishnaswami Alladi is professor of mathematics at the University of Florida, where he was the department chairman during 1998–2008. He received his PhD from the University of California, Los Angeles, in 1978. His research area is number theory, where he has made notable contributions. In 1987, during the Ramanujan Centennial in India, he got the inspiration to launch The Ramanujan Journal (now published by Springer), devoted to all areas of mathematics influenced by Ramanujan. He annually writes articles about Ramanujan and his place in the world of mathematics, for journals and newspapers. He is presently editor-in-chief of The Ramanujan Journal, editor of the book series Developments in Mathematics (Springer), and associate editor of Notices of the American Mathematical Society.
Mathematics --- Number theory --- wiskunde --- getallenleer
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The First Edition of the book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians in history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan's spectacular discoveries and remarkable life with the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. Also, among the articles are reviews of three important books on Ramanujan's mathematics and life. In addition, some aspects of Ramanujan's contributions, such as his remarkable formulae for the number pi, his path-breaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. This Second Edition is an expanded version of the first with six more articles by the author. Of note is the inclusion of a detailed review of the movie The Man Who Knew Infinity, a description of the fundamental work of the SASTRA Ramanujan Prize Winners, and an account of the Royal Society Conference to honour Ramanujan's legacy on the centenary of his election as FRS. KRISHNASWAMI ALLADI is professor of mathematics at the University of Florida where he was department chairman during 1998-2008. He received his PhD from the University of California, Los Angeles, in 1978. His area of research is number theory where he has made notable contributions. He is the Founder and Editor-in-Chief of The Ramanujan Journal (Springer), Founder and Editor of the book series Developments in Mathematics (Springer), and Chair of the SASTRA Ramanujan Prize Committee. He was an associate editor of Notices of the American Mathematical Society. From some Reviews of Edition 1 The book is an enlightening study of Ramanujan as a mathematician and as a human being and will appeal to mathematicians, students and the general public interested in mathematics. Themistocles M. Rassias, European Math. Soc. Newsletter, March 2013 A great book to go swimming in; Alladi has put together a sweeping compendium of essays on Ramanujan ... a wonderful book to browse through, and before you know it, you'll have read it all. ... This book is clearly entirely irresistible. Get a copy for yourself .... You can't miss. Michael Berg, Math. Assoc. of America Reviews, January 2013.
Pure sciences. Natural sciences (general) --- Number theory --- Mathematics --- History --- wetenschapsgeschiedenis --- geschiedenis --- wiskunde --- getallenleer
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This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at the University of Florida, Gainesville in March 2008. The success of this conference has led to annual year-long programs in Algebra, Number Theory, and Combinatorics (ANTC) at the university. A common theme in the book is the study of q-series, an area which in recent years has witnessed dramatic advances having significant impact on a variety of fields within and outside of mathematics such as physics. Most major aspects of the modern theory of q-series and how they relate to number theory, combinatorics, and special functions are represented in this volume. Topics include the theory of partitions via computer algebra, elementary asymptotic methods; expositions on Ramanujan's mock theta-functions emphasizing the classical aspects as well as the recent exciting connections with the theory of harmonic Maass forms; congruences for modular forms; a study of theta-functions from elementary, function-theoretic and Riemann surface viewpoints; and a systematic analysis of multiple basic hypergeometric functions associated with root systems of Lie algebras. The broad range of topics covered in this volume will be of interest to both researchers and graduate students who want to learn of recent developments in the theory of partitions, q-series and modular forms and their far reaching impact on diverse areas of mathematics.
Forms, Modular. --- Partitions (Mathematics). --- q-series. --- Partitions (Mathematics) --- q-series --- Forms, Modular, --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Forms, Modular --- Modular forms --- Mathematics. --- Special functions. --- Number theory. --- Combinatorics. --- Number Theory. --- Special Functions. --- Forms (Mathematics) --- Series --- Number theory --- Functions, special. --- Special functions --- Mathematical analysis --- Combinatorics --- Number study --- Numbers, Theory of
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Number theory --- Discrete mathematics --- Mathematics --- discrete wiskunde --- functies (wiskunde) --- wiskunde --- getallenleer
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