On discrete mean value of automorphic L-functions $$^{*}$$ ∗

Yu Chen and Weili Yao ()
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Yu Chen: Shanghai University
Weili Yao: Shanghai University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 377-387

Abstract: Abstract Let f be any normalized Hecke eigen forms with even integral weight $$k\ge 2$$ k ≥ 2 for the full modular group $$SL(2,{\mathbb {Z}})$$ S L ( 2 , Z ) , and $$\chi $$ χ be a primitive Dirichlet character modulo q. Let $$L_f(s,\chi )$$ L f ( s , χ ) be the automorphic L-function attached to f and $$\chi $$ χ . In this paper, we study the mean-square estimate of $$L_f(s,\chi )$$ L f ( s , χ ) weighted by incomplete character sums, via using properties of Fourier coefficients and analytic methods, and establish an asymptotic formula which refines the previous results.

Keywords: Automorphic L-function; Cusp form; Fourier coefficient; Dirichlet characters; 11F03; 11F11; 11F30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00371-9

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