On Dwork S P Adic Formal Congruences Theorem And Hypergeometric Mirror Maps
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On Dwork S P Adic Formal Congruences Theorem And Hypergeometric Mirror Maps
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Author : E. Delaygue
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-02-20
On Dwork S P Adic Formal Congruences Theorem And Hypergeometric Mirror Maps written by E. Delaygue 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 2017-02-20 with Mathematics categories.
Using Dwork's theory, the authors prove a broad generalization of his famous -adic formal congruences theorem. This enables them to prove certain -adic congruences for the generalized hypergeometric series with rational parameters; in particular, they hold for any prime number and not only for almost all primes. Furthermore, using Christol's functions, the authors provide an explicit formula for the “Eisenstein constant” of any hypergeometric series with rational parameters. As an application of these results, the authors obtain an arithmetic statement “on average” of a new type concerning the integrality of Taylor coefficients of the associated mirror maps. It contains all the similar univariate integrality results in the literature, with the exception of certain refinements that hold only in very particular cases.
Mirror Symmetry Ii
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Author : Brian Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Mirror Symmetry Ii written by Brian Greene 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 1997 with Mathematics categories.
Mirror Symmetry has undergone dramatic progress since the Mathematical Sciences Research Institute (MSRI) workshop in 1991, whose proceedings constitute voluem I of this continuing collection. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. Titles in this series are co-published, between the American Mathematical Society and International Press, Cambridge, MA, USA.
Foundations Of Computational Mathematics
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Author : Ronald A. DeVore
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-17
Foundations Of Computational Mathematics written by Ronald A. DeVore 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 2001-05-17 with Mathematics categories.
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Exponential Sums And Differential Equations
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 1990-09-21
Exponential Sums And Differential Equations written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-21 with Mathematics categories.
This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.
The Abel Prize 2013 2017
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Author : Helge Holden
language : en
Publisher: Springer
Release Date : 2019-02-23
The Abel Prize 2013 2017 written by Helge Holden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-23 with Mathematics categories.
The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.
The 1 2 3 Of Modular Forms
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Author : Jan Hendrik Bruinier
language : en
Publisher: Springer
Release Date : 2009-09-02
The 1 2 3 Of Modular Forms written by Jan Hendrik Bruinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Mathematics categories.
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
My Search For Ramanujan
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Author : Ken Ono
language : en
Publisher: Springer
Release Date : 2016-04-20
My Search For Ramanujan written by Ken Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Mathematics categories.
"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."
Creators Of Mathematical And Computational Sciences
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Author : Ravi P Agarwal
language : en
Publisher: Springer
Release Date : 2014-11-11
Creators Of Mathematical And Computational Sciences written by Ravi P Agarwal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.
The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.
Number Theory Ii
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Author : A. N. Parshin
language : en
Publisher: Springer
Release Date : 1992
Number Theory Ii written by A. N. Parshin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Volume 62 of the Encyclopedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Written for the nonspecialist, the author assumes a general understanding of modern algebra and elementary number theory. Only the general properties of algebraic number fields and relate.
The Shaping Of Arithmetic After C F Gauss S Disquisitiones Arithmeticae
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Author : Catherine Goldstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-03
The Shaping Of Arithmetic After C F Gauss S Disquisitiones Arithmeticae written by Catherine Goldstein 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 2007-02-03 with Mathematics categories.
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.