A converse theorem for epsilon factors

JOURNAL OF NUMBER THEORY

卷:89

Article

Kameswari, PA ; Tandon, R

关键词: local fields;    characters;    epsilon factors;   

DOI  :  10.1006/jnth.2000.2619

来源: Elsevier

【 摘 要 】

We prove the following theorem: Let F be a nonarchimedean local field of characteristic zero and K a quadratic extension of F. Let S be the set of characters of K* trivial on F*. Let chi (1) and chi (2) be two characters of K* such that chi (1 \) (F*) = chi (2 \F*) not equal 1. Let psi be a nontrivial additive character of F and psi (K) = psi tr (K/F). If epsilon(chi (1)lambda, psi (K)) = epsilon(chi (2)lambda, psi (K)) for all lambda is an element of S then chi (1) and chi (2) agree on all units in the ring of integers in K and on all elements of trace zero. If, in addition, the conductor of chi (1 \F*) is not zero then chi (1) = chi (2). (C) 2001 Academic Press.

【 授权许可】

Free