A p-adic analog of Hasse–Davenport product relation involving ϵ-factors

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Abstract

In this paper we prove some generalizations of the classical Hasse–Davenport product relation for certain arithmetic factors defined on a p-adic field F, among them one finds the ϵ-factors appearing in Tate’s thesis. We then show that these generalizations are equivalent to some representation theoretic identities relating the determinant of ramified local coefficients matrices defined for coverings of SL2(F) to Plancherel measures and γ-factors.

Original languageEnglish
JournalForum Mathematicum
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© 2024 Walter de Gruyter GmbH. All rights reserved.

Keywords

  • covering groups
  • epsilon factors
  • gamma factors
  • Hasse–Davenport product relation
  • local coefficients matrices
  • local factors
  • Whittaker spaces

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