Abstract
We prove a conjecture of Zagier, that the inverse Mellin transform of the symmetric square L-function attached to Ramanujan's tau function has an asymptotic expansion in terms of the zeros of the Riemann function.
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References
J. Jorgenson and S. Lang, Basic Analysis of Regularized Series and Products, Springer Lecture Notes vol. 1564.
G. Shimura, “On the holomorphy of certain Dirichlet series,” Proc. London Math. Soc. 31 (1975), 79–98.
E.C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd edn., Oxford University Press, 1986.
A. Voros, “Spectral functions, special functions and the Selberg zeta function,” Communications in Mathematical Physics 110 (1987), 439–465.
D.V. Widder, The Laplace Transform, Princeton University Press, 1941.
D. Zagier, “The Rankin-Selberg method for automorphic functions which are not of rapid decay,” J.-Fac.-Sci.-Univ.-Tokyo-Sect.-IA-Math. 28 (1981), 415–437.
D. Zagier, Modular forms of one variable, (notes based on a course given in Utrecht, Spring 1991).
D. Zagier, “Introduction to modular forms,” From number theory to physics (Les Houches, 1989), Springer, 1992, 238–291.s
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Hafner, J.L., Stopple, J. A Heat Kernel Associated to Ramanujan's Tau Function. The Ramanujan Journal 4, 123–128 (2000). https://doi.org/10.1023/A:1009886102576
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DOI: https://doi.org/10.1023/A:1009886102576