Leseprobe
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Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116
Nicholas M. Katz
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Skew-symmetric matrix, Variable (mathematics), Galois group, Big O notation, Existential quantification, Representation ring, Special case, Dual basis, Convolution, Convolution theorem, Endomorphism, Prime number, Algebraic group, Coefficient, Fundamental representation, Classification theorem, Zariski topology, Absolute value, Riemann hypothesis, Quotient group, Weil conjectures, Trace (linear algebra), Absolute Galois group, Conjugacy class, Cokernel, Monodromy theorem, Irreducibility (mathematics), Isomorphism class, Parameter, Sheaf (mathematics), Weyl character formula, Compactification (mathematics), Spin representation, Cartan subalgebra, Symplectic vector space, Kloosterman sum, Leray spectral sequence, Symplectic group, Multiplicative group, Representation theory, Lie algebra, Fundamental group, Integer, P-group, Finite field, Equidistribution theorem, Dimension (vector space), Residue field, Automorphic form, Characteristic polynomial, Abelian category, Adjoint representation, Lie theory, Tensor product, Cohomology, Exterior algebra, Automorphism, Theorem, Subgroup, Homomorphism, Complex Lie group, Frobenius endomorphism, Additive group, Maximal compact subgroup, Support (mathematics), Exponential sum, L-function, Monodromy, Affine variety, Gauss sum