RESEARCH ARTICLE

Oscillations of coefficients of symmetric square L-functions over primes

  • Fei HOU
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  • School of Mathematics, Shandong University, Jinan 250100, China

Received date: 30 Jul 2014

Accepted date: 05 Dec 2014

Published date: 12 Oct 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let L(s, sym2f) be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL(2,), with tf(n,1) denoting the nth coefficient of the Dirichlet series for it. It is proved that, for N≥2 and any α, there exists an effective positive constant c such that nNΛ(n)tf(n,1)e(nα)Nexp(clogN), where Λ(n) is the von Mangoldt function, and the implied constant only depends on f. We also study the analogue of Vinogradov’s three primes theorem associated to the coefficients of Rankin-Selberg L-functions.

Cite this article

Fei HOU . Oscillations of coefficients of symmetric square L-functions over primes[J]. Frontiers of Mathematics in China, 2015 , 10(6) : 1325 -1341 . DOI: 10.1007/s11464-015-0442-6

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