Twisted L Functions And Monodromy Am 150 PDF Download
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| Author | : Nicholas M. Katz |
| Publisher | : Princeton University Press |
| Total Pages | : 264 |
| Release | : 2009-01-10 |
| Genre | : Mathematics |
| ISBN | : 1400824885 |
Download Twisted L-Functions and Monodromy. (AM-150), Volume 150 Book in PDF, ePub and Kindle
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.
| Author | : Nicholas M. Katz |
| Publisher | : |
| Total Pages | : 249 |
| Release | : 1940 |
| Genre | : L-functions |
| ISBN | : 9780691091501 |
Download Annals of Mathematics Studies Book in PDF, ePub and Kindle
| Author | : Carlos J. Moreno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 313 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821842668 |
Download Advanced Analytic Number Theory: L-Functions Book in PDF, ePub and Kindle
Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
| Author | : Raoul Bott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 319 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475739516 |
Download Differential Forms in Algebraic Topology Book in PDF, ePub and Kindle
Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.
| Author | : Daniel Huybrechts |
| Publisher | : Cambridge University Press |
| Total Pages | : 499 |
| Release | : 2016-09-26 |
| Genre | : Mathematics |
| ISBN | : 1316797252 |
Download Lectures on K3 Surfaces Book in PDF, ePub and Kindle
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.
| Author | : Nicholas M. Katz |
| Publisher | : Princeton University Press |
| Total Pages | : 262 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 9780691084336 |
Download Gauss Sums, Kloosterman Sums, and Monodromy Groups Book in PDF, ePub and Kindle
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.
| Author | : Freydoon Shahidi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 218 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821849891 |
Download Eisenstein Series and Automorphic $L$-Functions Book in PDF, ePub and Kindle
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
| Author | : Joël Bellaïche |
| Publisher | : Springer Nature |
| Total Pages | : 319 |
| Release | : 2021-08-11 |
| Genre | : Mathematics |
| ISBN | : 3030772632 |
Download The Eigenbook Book in PDF, ePub and Kindle
This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.
| Author | : Edward Frenkel |
| Publisher | : Cambridge University Press |
| Total Pages | : 5 |
| Release | : 2007-06-28 |
| Genre | : Mathematics |
| ISBN | : 0521854431 |
Download Langlands Correspondence for Loop Groups Book in PDF, ePub and Kindle
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
| Author | : David Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387226397 |
Download The Geometry of Schemes Book in PDF, ePub and Kindle
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
