The Gross conjecture over rational function fields
We study the Gross conjecture for the cyclotomic function field extension k(∧f)/k where k = Fq(t) is the rational function field and f is a monic polynomial in Fq[t].We prove the conjecture in the Fermat curve case(i.e., when f = t(t - 1)) by a direct calculation. We also prove the case when f is irreducible, which is analogous to the Weil reciprocity law. In the general case, we manage to show the weak version of the Gross conjecture here.
作 者： OUYANG Yi 作者单位： Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China 刊 名： 中国科学A辑（英文版） SCI 英文刊名： SCIENCE IN CHINA SERIES A (MATHEMATICS) 年，卷(期)： 2005 48(12) 分类号： O1 关键词： Gross conjecture L-function Theta-function Weil reciprocity