ALGEBRAIC TWISTS OF GL3 ×GL2 L-FUNCTIONS

Yongxiao Lin; Philippe Michel; Will Sawin

doi:10.1353/ajm.2023.0015

ALGEBRAIC TWISTS OF GL₃ ×GL₂ L-FUNCTIONS

Yongxiao Lin
, Philippe Michel
, Will Sawin

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

6 Scopus citations

Abstract

We prove that the coefficients of a GL₃ ×GL₂ Rankin–Selberg L-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result of Fouvry, Kowalski, and Michel for GL₂ and of Kowalski, Lin, Michel, and Sawin for GL₃ . This result is inspired by a recent work of P. Sharma who discussed the case of a Dirichlet character of prime modulus.

Original language	English (US)
Pages (from-to)	585-645
Number of pages	61
Journal	American Journal of Mathematics
Volume	145
Issue number	2
DOIs	https://doi.org/10.1353/ajm.2023.0015
State	Published - Apr 2023
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1353/ajm.2023.0015

Cite this

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abstract = "We prove that the coefficients of a GL3 ×GL2 Rankin–Selberg L-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result of Fouvry, Kowalski, and Michel for GL2 and of Kowalski, Lin, Michel, and Sawin for GL3 . This result is inspired by a recent work of P. Sharma who discussed the case of a Dirichlet character of prime modulus.",

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AB - We prove that the coefficients of a GL3 ×GL2 Rankin–Selberg L-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result of Fouvry, Kowalski, and Michel for GL2 and of Kowalski, Lin, Michel, and Sawin for GL3 . This result is inspired by a recent work of P. Sharma who discussed the case of a Dirichlet character of prime modulus.

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ALGEBRAIC TWISTS OF GL₃ ×GL₂ L-FUNCTIONS

Abstract

All Science Journal Classification (ASJC) codes

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