JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 72-77.doi: 10.6040/j.issn.1671-9352.0.2021.603

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Estimate involving sum of coefficients of the Rankin-Selberg L-function

LIU Can   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Published:2022-01-07

Abstract: Let k be an even integer and f(z) be a primitive holomorphic cusp form of weight k for the full modular group Γ=SL2(Z). Let λsym2f ×sym3f(n)be the n-th coefficient of Dirichlet series of the Rankin-Selberg L-function L(s,sym2f ×sym3f). Using the breakthroughs of Newton-Thorne on the automorphy of L(s,symjf)on j to study the mean distribution of λ2sym2f ×sym3f(n), a more accurate asymptotic formula can be obtained.

Key words: holomorphic cusp forms, Rankin-Selberg L-function, symmetric power L-function

CLC Number: 

  • O156.4
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