The Gross conjecture over rational f

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  

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