In this paper, we study the remaining parts, namely, we give such bounds for modular forms with Fourier coefficients in an arbitrary algebraic number field
K and for any prime ideal p in K.
i) The usual definition is more general, the coefficients of S can be taken in an arbitrary algebraic number field
Let p be an odd prime and k an algebraic number field
of finite degree such that the p-rank of Cl(k) is equal to 2.
presents an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field
, point set topological spaces, and classical noncommutative localization.
of Tokyo) explore similarities between algebraic number fields
and algebraic function fields in one variable over finite fields, explain adele rings and idele groups, derive several prime number theorems, and prove the main theorem of class field theory.
Stan, Florin, University of Illinois, Urbana-Champaign, Trace problems in algebraic number fields
and applications to characters of finite groups.