Lower order terms for the one-level densities of symmetric power $L$-functions in the level aspect

Guillaume Ricotta; Emmanuel Royer

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arXiv · 0806.2908

Lower order terms for the one-level densities of symmetric power $L$-functions in the level aspect

Guillaume Ricotta·Emmanuel Royer

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Abstract

In a previous paper, the authors determined, among other things, the main terms for the one-level densities for low-lying zeros of symmetric power L-functions in the level aspect. In this paper, the lower order terms of these one-level densities are found. The combinatorial difficulties, which should arise in such context, are drastically reduced thanks to Chebyshev polynomials, which are the characters of the irreducible representations of SU(2). %

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Guillaume Ricotta, Emmanuel Royer. 2008-06-18. Lower order terms for the one-level densities of symmetric power $L$-functions in the level aspect. https://arxiv.org/abs/0806.2908

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