A constraint for twist equivalence of cusp forms on GL(n)

Dinakar Ramakrishnan; Liyang Yang

doi:10.7169/FACM/1913

A constraint for twist equivalence of cusp forms on GL(n)

Dinakar Ramakrishnan, Liyang Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This note answers, and generalizes, a question of Kaisa Matomäki. We show that given two cuspidal automorphic representations π₁ and π₂ of GL(n) over a number field F of respective conductors N₁, N₂, every character χ such that π1 χ ' π₂ of conductor Q, satisfies the bound: Qⁿ | N₁N₂. If at every finite place v, π1_,v is a discrete series whenever it is ramified, then Qⁿ divides the least common multiple [N₁, N₂].

Original language	English (US)
Pages (from-to)	105-117
Number of pages	13
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	65
Issue number	1
DOIs	https://doi.org/10.7169/FACM/1913
State	Published - Sep 2021

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Conductor
Cusp forms
GL(n)
Twist equivalence

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AB - This note answers, and generalizes, a question of Kaisa Matomäki. We show that given two cuspidal automorphic representations π1 and π2 of GL(n) over a number field F of respective conductors N1, N2, every character χ such that π1 χ ' π2 of conductor Q, satisfies the bound: Qn | N1N2. If at every finite place v, π1,v is a discrete series whenever it is ramified, then Qn divides the least common multiple [N1, N2].

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KW - Twist equivalence

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A constraint for twist equivalence of cusp forms on GL(n)

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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