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2011•Canadian Journal of MathematicsOpen access

On Higher Moments of Fourier Coefficients of Holomorphic Cusp Forms

Guangshi Lü

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Abstract

Abstract Let be the space of holomorphic cusp forms of even integral weight k for the full modular group. Let and be the n-th normalized Fourier coefficients of two holomorphic Hecke eigencuspforms , respectively. In this paper we are able to show the following results about higher moments of Fourier coefficients of holomorphic cusp forms. (i)For any , we have (ii)If , then for any , we have If , then for any , we have If and , then for any , we have where P(x) is a polynomial of degree 3.

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Abstract Let be the space of holomorphic cusp forms of even integral weight k for the full modular group. Let and be the n-th normalized Fourier coefficients of two holomorphic Hecke eigencuspforms , respectively. In this paper we are able to show the following results about higher moments of Fourier coefficients of holomorphic cusp forms. (i)For any , we have (ii)If , then for any , we have If , then for any , we have If and , then for any , we have where P(x) is a polynomial of degree 3.

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Available abstract

Abstract Let be the space of holomorphic cusp forms of even integral weight k for the full modular group. Let and be the n-th normalized Fourier coefficients of two holomorphic Hecke eigencuspforms , respectively. In this paper we are able to show the following results about higher moments of Fourier coefficients of holomorphic cusp forms. (i)For any , we have (ii)If , then for any , we have If , then for any , we have If and , then for any , we have where P(x) is a polynomial of degree 3.

Key concepts: Holomorphic function, Cusp (singularity), Mathematics, Cusp form, Modular form, Fourier series, Pure mathematics, Polynomial

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