Leseprobe
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Convolution and Equidistribution
Nicholas M. Katz
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.
The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods.
By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
Kundenbewertungen
Complex conjugate, Integer, Scientific notation, Uniform convergence, Trivial representation, Subobject, Coefficient, Overview (debate), Indecomposability, Connectedness, Linear combination, Pullback (differential geometry), Haar measure, Summation, Automorphism, Monic polynomial, Reductive group, Orthogonal group, Semidirect product, Symplectic group, Tensor, Convolution, Conjugacy class, Theorem, Derived category, Special case, Functor, Duality (mathematics), Maximal compact subgroup, Eigenvalues and eigenvectors, Prime number, Polynomial, Tensor product, Abelian category, Subcategory, Monodromy, Contradiction, Finite morphism, Addition, Finite field, Corollary, One-dimensional space, Dense set, Absolute value, Lie algebra, Morphism, Orthogonality, Commutator subgroup, Dimension (vector space), Fourier transform, Gauss sum, Normal subgroup, Subgroup, Adjunction (field theory), Determinant, Perverse sheaf, Irreducible representation, Tannakian category, Identity component, Sheaf (mathematics), Change of base, GEOM, Point at infinity, Residue field, Diagram (category theory), Isomorphism class, Group theory, Probability measure, Pullback, Root of unity