Download or read book Gauss Sums Kloosterman Sums and Monodromy Groups AM 116 Volume 116 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2016-03-02 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Probabilistic Number Theory written by Emmanuel Kowalski and published by Cambridge University Press. This book was released on 2021-05-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
Download or read book Rigid Local Systems AM 139 Volume 139 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2016-03-02 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Proceedings IEEE International Symposium on Information Theory written by and published by . This book was released on 1998 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 1998 IEEE International Symposium on Information Theory written by and published by Institute of Electrical & Electronics Engineers(IEEE). This book was released on 1998 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Download or read book IEEE International Symposium on Information Theory written by and published by . This book was released on 1998 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Books in Series written by and published by . This book was released on 1985 with total page 1404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1980- issued in three parts: Series, Authors, and Titles.
Download or read book Gauss Sums Kloosterman Sums and Monodromy Groups written by Nicholas M. Katz and published by Princeton University Press. This book was released on 1988 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analytic Number Theory written by Henryk Iwaniec and published by American Mathematical Soc.. This book was released on 2021-10-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Download or read book Seminar on Transformation Groups written by Armand Borel and published by Princeton University Press. This book was released on 1960 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar on Transformation Groups. (AM-46), Volume 46, will be forthcoming.
Download or read book Twisted L Functions and Monodromy AM 150 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2002-02-24 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scientific and Technical Books and Serials in Print written by and published by . This book was released on 1989 with total page 1216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Forthcoming Books written by Rose Arny and published by . This book was released on 1988-09 with total page 2174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Probabilistic Number Theory written by Emmanuel Kowalski and published by Cambridge University Press. This book was released on 2021-05-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
Download or read book Books in Print written by and published by . This book was released on 1987 with total page 2204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
