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Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116
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Nicholas M. Katz
Nicholas M. KatzSearch for this author in:
Language:
English
Published/Copyright:
1988
About this book
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.
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 2, 2016
eBook ISBN:
9781400882120
Pages and Images/Illustrations in book
Main content:
256
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eBook ISBN:
9781400882120
Keywords for this book
Exponential sum; Monodromy; Convolution; Sheaf (mathematics); Subgroup; Cohomology; Kloosterman sum; Residue field; Prime number; Dimension (vector space); Finite field; Conjugacy class; Characteristic polynomial; Gauss sum; Classification theorem; Equidistribution theorem; Isomorphism class; Lie algebra; Trace (linear algebra); Leray spectral sequence; Coefficient; Automorphic form; Compactification (mathematics); Weil conjectures; Zariski topology; Symplectic vector space; Additive group; Existential quantification; Tensor product; Weyl character formula; Convolution theorem; Automorphism; Monodromy theorem; Absolute Galois group; Fundamental group; Theorem; Parameter; Riemann hypothesis; Variable (mathematics); Absolute value; Cartan subalgebra; Abelian category; Frobenius endomorphism; Integer; Special case; Representation ring; Symplectic group; Exterior algebra; Complex Lie group; Support (mathematics); Adjoint representation; Fundamental representation; Quotient group; Galois group; Multiplicative group; Skew-symmetric matrix; Maximal compact subgroup; Representation theory; Irreducibility (mathematics); Spin representation; P-group; Algebraic group; L-function; Homomorphism; Lie theory; Cokernel; Affine variety; Dual basis; Big O notation; Endomorphism
Audience(s) for this book
College/higher education;Professional and scholarly;
