Asymptotics of class number and genus for abelian extensions of an algebraic function field

JOURNAL OF NUMBER THEORY

卷:132

Article

Ward, Kenneth

关键词: Finite field;    Congruence function field;    Abelian extension;    Class number;    Genus;    Asymptotic;   

DOI  :  10.1016/j.jnt.2012.05.016

来源: Elsevier

【 摘 要 】

Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established: namely, for such extensions with class number h, genus g, and field of constants F, that In h similar to g In vertical bar F vertical bar. The proof is completely classical, employing well known results from congruence function field theory. This gives an answer to a question of E. Inaba. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free