Work

Zeros of polynomials in derivatives of automorphic L‐functions

Year: 2026

Type: article

Abstract: Let be the set of all cuspidal automorphic representations of , and let be a polynomial in the derivatives of ‐functions associated with representations . We establish an asymptotic formula for the number of nontrivial zeros of with . We explicitly determine the main term of this formula in terms of the dimensions, the arithmetic conductors, and the orders of differentiation of the component ‐functions. Furthermore, we show that, under certain conditions, almost all nontrivial zeros of lie near the critical line .

Source: Mathematika

DOI: 10.1112/mtk.70120

Authors: Anji Dong, Nawapan Wattanawanichkul, Alexandru Zaharescu

Institutions: University of Illinois Urbana-Champaign, IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

OpenAlex ID: W7171921182

FWCI:

Cites: 19

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