Abstract
In this paper, we give improvements on the error terms of asymptotic formulas for averages of coefficients of certain degree five and degree seven L-functions that can be factorized as a product of degree one and Rankin–Selberg L-functions.
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References
V. Blomer, R. Khan, and M. Young, Distribution of mass of holomorphic cusp forms, Duke Math. J., 162(14):2609–2644, 2013.
A. Dasgupta, W. Leung, and M. Young, The second moment of the GL3 standard L-function on the critical line, preprint, arXiv:2407.06962.
J. Friedlander and H. Iwaniec, Summation formulae for coefficients of L-functions, Can. J. Math., 57(3):494–505, 2005.
B. Huang, On the Rankin–Selberg problem, Math. Ann., 381(3–4):1217–1251, 2021.
B. Huang, On the Rankin–Selberg problem. II, Q. J. Math., 75(1):1–10, 2024.
B. Huang, Y. Lin, and Z.Wang, Averages of coefficients of a class of degree 3 L-functions, Ramanujan J., 57(1):79–91, 2022.
B. Huang, Q. Sun, and H. Zhang, Analytic twists of GL2 × GL2 automorphic forms, Math. Nachr., 296(6):2366–2394, 2023.
H. Kim and F. Shahidi, Functorial products for GL2 × GL3 and the symmetric cube for GL2, Ann.Math. (2), 155(3): 837–893, 2002.With an appendix by Colin J. Bushnell and Guy Henniart.
Y. Lin and Q. Sun, Analytic twists of GL3 × GL2 automorphic forms, Int. Math. Res. Not., 2021(19):15143–15208, 2021.
S. Pal, Second moment of degree three L-functions, preprint, arXiv:2212.14620v2.
E. Kıral, I. Petrow, and M. Young, Oscillatory integrals with uniformity in parameters, J. Théor. Nombres Bordx., 31(1):145–159, 2019.
D. Ramakrishnan, Modularity of the Rankin-Selberg L-series, andmultiplicity one for SL(2), Ann.Math. (2), 152(1): 45–111, 2000.
E.C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Clarendon Press, Oxford, 1986.With a preface by D.R. Heath-Brown.
H. Zhang, Averages of coefficients of a class of degree seven L-functions, J. Number Theory, 253:137–156, 2023.
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This work is in part supported by the National Key Research and Development Program of China (No. 2021YFA1000700), NSFC (No. 12031008), and China Scholarship Council (No. 202206220071).
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Zhang, H. Averages of coefficients of certain degree five and seven L-functions. Lith Math J (2025). https://doi.org/10.1007/s10986-025-09661-7
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DOI: https://doi.org/10.1007/s10986-025-09661-7