Abstract
By applying the formula for essential Whittaker functions established by Matringe and Miyauchi, we study five integral representations for irreducible admissible generic representations of GLn over p-adic fields. In each case, we show that the integrals achieve local formal L-functions defined by Langlands parameters, when the test vector is associated to the new form. We give the relation between local periods involving essential Whittaker functions and special values of formal L-factors at (Formula presented.) for certain distinguished or unitary representations. The period integrals are also served as standard nonzero distinguished forms.
Original language | English |
---|---|
Pages (from-to) | 339-367 |
Number of pages | 29 |
Journal | Mathematische Nachrichten |
Volume | 296 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2023 |
Bibliographical note
Publisher Copyright:© 2022 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH.
Keywords
- local Rankin–Selberg L-functions
- local period integrals
- newforms
- test vector problems