On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields
| Autor: | Jingsong Chai, Zhi Qi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Complex field Conjecture Mathematics - Number Theory 010102 general mathematics Automorphic form 11F37 11F67 11F70 Algebraic number field 01 natural sciences Ramanujan's sum symbols.namesake Metaplectic group 0103 physical sciences FOS: Mathematics symbols Number Theory (math.NT) 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Analysis Bessel function Mathematics - Representation Theory Mathematics |
| Popis: | In this paper, by inputting the Bessel identities over the complex field in previous work of the authors, the Waldspurger formula of Baruch and Mao is extended from totally real fields to arbitrary number fields. This is applied to give a non-trivial bound towards the Ramanujan conjecture for automorphic forms of the metaplectic group $\widetilde{\mathrm{SL}}_2$ for the first time in the generality of arbitrary number fields. 22 pages. To appear in J. Funct. Anal |
| Databáze: | OpenAIRE |
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