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

Author

Listed:
  • Yu Chen

    (Shanghai University)

  • Weili Yao

    (Shanghai University)

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.

Suggested Citation

  • Yu Chen & Weili Yao, 2024. "On discrete mean value of automorphic L-functions $$^{*}$$ ∗," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(1), pages 377-387, March.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:1:d:10.1007_s13226-023-00371-9
    DOI: 10.1007/s13226-023-00371-9
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