Transformation formula for exponential sums involving fourier coefficients of modular forms

CS, Yogananda (1993) Transformation formula for exponential sums involving fourier coefficients of modular forms. In: Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 103 (1). pp. 1-25.

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Abstract

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences - Mathematical Sciences
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian Academy of Sciences.
Keywords:	Exponential sums;summation formula;cusp forms and Maass forms ;transformation formula
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	14 Mar 2011 08:41
Last Modified:	14 Mar 2011 08:41
URI:	http://eprints.iisc.ac.in/id/eprint/35956

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