Oscillations of coefficients of symmetric square L-functions over primes

doi:10.1007/s11464-015-0442-6

Front. Math. China

2015, Vol. 10

Issue (6) : 1325-1341 https://doi.org/10.1007/s11464-015-0442-6

RESEARCH ARTICLE

Oscillations of coefficients of symmetric square L-functions over primes

Fei HOU(

)

School of Mathematics, Shandong University, Jinan 250100, China

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Abstract

Let L(s, sym²f) be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL(2,?), with t_f(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 ∑n≤NΛ(n)tf(n,1)e(nα)≪Nexp⁡(−clog⁡N), 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.

Keywords symmetric-square L-function primitive holomorphic cusp form Fourier coefficient

Corresponding Author(s): Fei HOU

Issue Date: 12 October 2015

Cite this article:

Fei HOU. Oscillations of coefficients of symmetric square L-functions over primes[J]. Front. Math. China, 2015, 10(6): 1325-1341.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0442-6
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I6/1325

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