Abstract
In this note, we present a simple approach for bounding the shifted convolution sum involving the Fourier coefficients of half-integral weight holomorphic cusp forms and Maass cusp forms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blomer V. Sums of Hecke eigenvalues over values of quadratic polynomials. Int Math Res Not, 2008, 16: 1–29
Duke W, Iwaniec H. Bilinear forms in the Fourier coefficients of half-integral weight cusp forms and sums over primes. Math Ann, 1990, 286: 783–802
Goldfeld D. Analytic and arithmetic theory of Poincaré series. Astérisque, 1979, 61: 95–107
Good A. Cusp forms and eigenfunctions of the Laplacian. Math Ann, 1981, 255: 523–548
Gradshtein I S, Ryzhik I M. Tables of Integrals, Series and Products. New York-London: Academic Press, 1965
Hafner J L. Explicit estimates in the arithmetic theory of cusp forms and Poincaré series. Math Ann, 1983, 264: 9–20
Iwaniec H. Fourier coefficients of modular forms of half-integral weight. Invent Math, 1987, 87: 385–401
Luo W. Zeros of Hecke L-functions associated with cusp forms. Acta Arith, 1995, 71: 139–158
Meurman T. On exponential sums involving the Fourier coefficients of Maass wave forms. J Reine Angew Math, 1988, 384: 192–207
Selberg A. On the estimation of Fourier coefficients of modular forms. In: Proc Symp Pure Math, Vol. VIII, Theory of Numbers. Providence, RI: American Mathematical Society, 1965, 1–15
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday
Rights and permissions
About this article
Cite this article
Luo, W. On shifted convolution of half-integral weight cusp forms. Sci. China Math. 53, 2411–2416 (2010). https://doi.org/10.1007/s11425-010-4038-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-010-4038-z