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A Converse Theorem for Epsilon Factors

โœ Scribed by P.Anuradha Kameswari; Rajat Tandon

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
156 KB
Volume
89
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

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 / 1 and / 2 be two characters of K* such that / 1 | F * =/ 2 | F * {1. Let be a nontrivial additive character of F and K = b tr Kร‚F . If =(/ 1 *, K )= =(/ 2 *, K ) for all * # S then / 1 and / 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 / 1 | F * is not zero then / 1 =/ 2 .

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