Gauss Sums Kloosterman Sums And Monodromy Groups Am 116 Volume 116
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Gauss Sums Kloosterman Sums And Monodromy Groups Am 116 Volume 116
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Gauss Sums Kloosterman Sums And Monodromy Groups Am 116 Volume 116 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 2016-03-02 with Mathematics categories.
The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
Gauss Sums Kloosterman Sums And Monodromy Groups
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 1988
Gauss Sums Kloosterman Sums And Monodromy Groups 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 1988 with Mathematics categories.
The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
Twisted L Functions And Monodromy Am 150 Volume 150
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
Twisted L Functions And Monodromy Am 150 Volume 150 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 2009-01-10 with Mathematics categories.
For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
An Introduction To Probabilistic Number Theory
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Author : Emmanuel Kowalski
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-06
An Introduction To Probabilistic Number Theory written by Emmanuel Kowalski 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 2021-05-06 with Mathematics categories.
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
Rigid Local Systems Am 139 Volume 139
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Rigid Local Systems Am 139 Volume 139 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 2016-03-02 with Mathematics categories.
Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform.
Proceedings Ieee International Symposium On Information Theory
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Author :
language : en
Publisher:
Release Date : 1998
Proceedings Ieee International Symposium On Information Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Information theory categories.
1998 Ieee International Symposium On Information Theory
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Author :
language : en
Publisher: Institute of Electrical & Electronics Engineers(IEEE)
Release Date : 1998
1998 Ieee International Symposium On Information Theory written by and has been published by Institute of Electrical & Electronics Engineers(IEEE) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computers categories.
The special theme of ISIT '98 is the 50th anniversary of the founding of the field of information theory in Claude Shannon's 1948 paper, A Mathematical Theory of Communication. Topics in these papers on the conference include nomadic computing, and CDMA in war and peace."
Ieee International Symposium On Information Theory
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Author :
language : en
Publisher:
Release Date : 1998
Ieee International Symposium On Information Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Information theory categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
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 2004 with Mathematics categories.
Books In Series
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Author :
language : en
Publisher:
Release Date : 1985
Books In Series written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Monographic series categories.
Vols. for 1980- issued in three parts: Series, Authors, and Titles.