Leseprobe
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Exponential Sums and Differential Equations. (AM-124), Volume 124
Nicholas M. Katz
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.
Kundenbewertungen
Irreducible representation, Surjective function, Trichotomy (mathematics), Subgroup, Exponential sum, Symmetric group, Ring homomorphism, Adjoint representation, Lie algebra, Field of fractions, Special case, Unitarian trick, Irreducibility (mathematics), Eigenvalues and eigenvectors, Equation, Galois extension, Mathematical induction, Isogeny, Polynomial, Set (mathematics), Isomorphism class, Big O notation, Three-dimensional space (mathematics), Permutation, P-adic number, Reductive group, Maximal compact subgroup, Diagram (category theory), Galois group, Hypergeometric function, Calculation, Identity element, Monomial, Homomorphism, Quotient group, Algebraic integer, Matrix coefficient, Cohomology, Comparison theorem, Fourier transform, Torsor (algebraic geometry), Monodromy theorem, Sheaf (mathematics), Bijection, Differential equation, Prime number, Theorem, Conjugacy class, Gauss sum, Automorphism, Convolution, Logarithm, Monic polynomial, Variable (mathematics), Formal power series, Root of unity, Dimension (vector space), Existential quantification, Fundamental representation, Characteristic polynomial, Representation theory, Summation, Differential Galois theory, Codimension, Tensor product, Coefficient, Fundamental group, Laurent polynomial, Algebraically closed field, Monodromy