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An Introduction to Congruences Between Modular Forms
The Cyclotomic Problem
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2000 Mathematics subject A-module Artin assume Aut(X automorphism base change bound character characteristic class field coefficients cohomology complex congruence primes conjecture 3.2 conjugacy classes Corollary corresponding cusp forms cyclotomic numbers cyclotomic problem defined Definition degree denote diophantine divisor Drinfeld modules eigenform elements elliptic curves equals the number exists finite fields formula function field functional equation Gauss genus given group algebra group G group rings Hecke operators Hence holomorphic implies infinite integral solutions irreducible isomorphism Jacobi sums L-function lattice Lemma Math Mathematics subject classification matrices modular forms multiplicative nilpotent non-zero number field Number Theory numbers of order obtained polynomial positive integer prime ideal proof Proposition proved quadratic field rank real number representation residue result Riemann Rogers-Ramanujan identities root number satisfies semisimple sequence Shimura subgroup subsequence of length Suppose tion torsion trivial unramified view-obstruction problem zero zero-sum subsequence zeta function