On the coefficients of symmetric power $L$-functions

Jaban Meher; Karam Deo Shankhadhar; G. K. Viswanadham

On the coefficients of symmetric power $L$-functions

Number Theory 2017-10-13 v3

Authors: Jaban Meher , Karam Deo Shankhadhar , G. K. Viswanadham

Abstract

We study the signs of the Fourier coefficients of a newform. Let $f$ be a normalized newform of weight $k$ for $\Gamma_0(N)$ . Let $a_f(n)$ be the $n$ th Fourier coefficient of $f$ . For any fixed positive integer $m$ , we study the distribution of the signs of $\{a_f(p^m)\}_p$ , where $p$ runs over all prime numbers. We also find out the abscissas of absolute convergence of two Dirichlet series with coefficients involving the Fourier coefficients of cusp forms and the coefficients of symmetric power $L$ -functions.

Keywords

symmetric power L-functions Fourier coefficients newforms sign distribution Dirichlet series abscissa of absolute convergence

Cite

@article{arxiv.1703.08344,
  title  = {On the coefficients of symmetric power $L$-functions},
  author = {Jaban Meher and Karam Deo Shankhadhar and G. K. Viswanadham},
  journal= {arXiv preprint arXiv:1703.08344},
  year   = {2017}
}

On the coefficients of symmetric power $L$-functions

Abstract

Keywords

Cite

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