TL;DR
This paper presents a concise proof of the Lamprecht-Tate formula for epsilon factors of multiplicative characters over non-Archimedean local fields, and demonstrates its relation to Deligne's twisting formula.
Contribution
Provides a simplified proof of the Lamprecht-Tate formula and connects it to Deligne's twisting formula as a special case.
Findings
Short and elegant proof of the Lamprecht-Tate formula
Shows the relation between Lamprecht-Tate and Deligne's twisting formula
Clarifies the role of epsilon factors in local field character theory
Abstract
For multiplicative characters of a non-Archimedean local field, we have a formula for epsilon factors due to John Tate. Before Tate, Erich Lamprecht also gave a formula for local epsilon factors of linear characters. Then Tate generalizes the formula for epsilon factors. In this paper, we give a very short and neat proof of the Lamprecht-Tate formula. We also show that the famous twisting formula of Deligne is a special case of the Lamprecht-Tate formula.
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Taxonomy
TopicsMathematical and Theoretical Analysis · advanced mathematical theories · Advanced Algebra and Geometry