Gauss Sums Kloosterman Sums and Monodromy Groups AM 116 Volume 116

1. Gaussian sums. 2 . Kloosterman sums. 3. Homology theory. 4. Monodromy groups. I. Title. II. Series: Annals of mathematics studies ; no. 116. QA246.8.G38K37 1987 512'.7 87-45525 ISBN 0-691-08432-7 (alk. paper) ISBN 0-691-08433-5 (pbk.) ...

Author: Nicholas M. Katz

Publisher: Princeton University Press

ISBN: 1400882125

Category: Mathematics

Page: 256

View: 176

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

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: Nicholas M. Katz

Publisher: Princeton University Press

ISBN: 9780691084336

Category: Mathematics

Page: 262

View: 512

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.

Handbook of Finite Fields

<688, 689, 703> [1693] M. Kassabov, A. Lubotzky, and N. Nikolov, Finite simple groups as expanders, Proc. Natl. ... <156, 161, 164, 169> [1701] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, volume 116 of Annals of ...

Author: Gary L. Mullen

Publisher: CRC Press

ISBN: 1439873828

Category: Computers

Page: 1068

View: 139

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Finite Fields Theory and Computation

1518 , Springer - Verlag , Berlin , 1992 , pp . 82-98 . 1456. KATZ N.M. , Gauss sums , Kloosterman sums , and monodromy groups , Ann . of Math . Studies , vol . 116 , Princeton Univ . Press , 1988 . 1457 . An estimate for character sums ...

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

ISBN: 9780792356622

Category: Mathematics

Page: 560

View: 428

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.

Analysis at Large

Katz, N.M.: Gauss sums, Kloosterman sums and monodromy groups. Annals of Math. Studies, vol. 116. Princeton Univ. Press (1988) 21. Katz, N.M.: Perversity and exponential sums. In: Algebraic Number Theory in honor of K. Iwasawa.

Author: Artur Avila

Publisher: Springer Nature

ISBN: 3031053311

Category: Mathematics

Page: 388

View: 896

​Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prékopa-Leindler inequality and sumsets with quasicubes, the fractal uncertainty principle for the Walsh-Fourier transform, the continuous formulation of shallow neural networks as Wasserstein-type gradient flows, logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators, polynomial equations in subgroups, trace sets of restricted continued fraction semigroups, exponential sums, twisted multiplicativity and moments, the ternary Goldbach problem, as well as the multiplicative group generated by two primes in Z/QZ. It is hoped that this volume will inspire further research in the areas of analysis treated in this book and also provide direction and guidance for upcoming developments in this essential subject of mathematics.

Random Matrices Frobenius Eigenvalues and Monodromy

Katz , N. , Gauss sums , Kloosterman sums , and monodromy groups , Ann . of Math . Studies , vol . 116 , Princeton Univ . Press , 1988 . Katz , N. , and Lang , S. , Finiteness theorems in geometric classfield theory , L'Enseignment Math ...

Author: Nicholas M. Katz

Publisher: American Mathematical Soc.

ISBN: 9780821869611

Category: Mathematics

Page: 454

View: 329


Sequences and Their Applications SETA 2010

C. R. Acad. Sci. Paris Sér. I. Math. 309(11), 723–726 (1989) 9. Katz, N.M.: Gauss sums, Kloosterman sums, and monodromy groups. Annals of Mathematics Studies, vol. 116. Princeton University Press, Princeton (1988) Lachaud, G., Wolfmann, ...

Author: Claude Carlet

Publisher: Springer

ISBN: 3642158749

Category: Computers

Page: 465

View: 951

This book constitutes the proceedings of the 6th International Conference on Sequences and Their Applications held in Paris, France, in September 2010.

Surveys in Number Theory

[46] N. Katz, Gauss sums, Kloosterman sums and Monodromy Groups, Ann. of Math. Stud., vol. 116, Princeton University Press, Princeton, 1988. [47] ______ , Travaux de Laumon, Asterisque 161-162 (1988), 105-132, Seminaire Bourbaki, ...

Author: Bruce Berndt

Publisher: CRC Press

ISBN: 1000065286

Category: Mathematics

Page: 368

View: 898

This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research. It serves as an inspiration to graduate students and as a reference for research mathematicians.

The Abel Prize 2013 2017

Gauss sums, Kloosterman sums, and monodromy groups, volume 116 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 1988. N. M. Katz and G. Laumon. Transformation de Fourier et majoration de sommes exponentielles ...

Author: Helge Holden

Publisher: Springer

ISBN: 3319990284

Category: Mathematics

Page: 774

View: 239

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.

Zeta Functions in Algebra and Geometry

MR885774 (88i:11053) 8. , Gauss Sums, Kloosterman Sums, and Monodromy Groups, Annals of Mathematics Studies, vol. 116, Princeton University Press, 1988. MR955052 (91a:11028) 9. , Exponential Sums and Differential Equations, ...

Author: Antonio Campillo

Publisher: American Mathematical Soc.

ISBN: 0821869000

Category: Algebraic varieties

Page: 344

View: 850

The volume contains the proceedings of the ``Second International Workshop on Zeta Functions in Algebra and Geometry'' held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).