Algebraic twists of $\mathrm{GL}_3\times \mathrm{GL}_2$ $L$-functions

Yongxiao Lin; Philippe Michel; Will Sawin

Algebraic twists of $\mathrm{GL}_3\times \mathrm{GL}_2$ $L$-functions

Number Theory 2022-04-20 v3 Algebraic Geometry

Authors: Yongxiao Lin , Philippe Michel , Will Sawin

Abstract

We prove that the coefficients of a $\mathrm{GL}_3\times \mathrm{GL}_2$ Rankin--Selberg $L$ -function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result \cite{FKM1} for~ $\mathrm{GL}_2$ and \cite{KLMS} for $\mathrm{GL}_3$ . This result is inspired by a recent work of P. Sharma who discussed the case of a Dirichlet character of prime modulus.

Keywords

gl3 x gl2 l-functions rankin-selberg l-functions trace functions interstellar extinction small conductor algebraic twists prime modulus

Cite

@article{arxiv.1912.09473,
  title  = {Algebraic twists of $\mathrm{GL}_3\times \mathrm{GL}_2$ $L$-functions},
  author = {Yongxiao Lin and Philippe Michel and Will Sawin},
  journal= {arXiv preprint arXiv:1912.09473},
  year   = {2022}
}

Comments

46 pages; final version; to appear in Amer. Journ. Math

Algebraic twists of $\mathrm{GL}_3\times \mathrm{GL}_2$ $L$-functions

Abstract

Keywords

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