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On some exponential sums connected with Ramanujan's τ-function

Published online by Cambridge University Press:  26 February 2010

A. Perelli
A. Perelli
Affiliation:
Istituto di Matematica, Universitá di Genova, Via L.B. Alberti 4, 16132 Genova, Italy.
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Extract

In a recent paper, Parson and Sheingorn [11[ gave some estimates for certain exponential sums associated with Ramanujan's τ-function and, in general, with the Fourier coefficients of the cusp forms for the full modular group which are eigenfunctions for the Hecke operators. The exponential sums considered in that paper are closely connected with the exponential sum

where α ∈ ℝ and e(θ) = e2πiθ, and the methods used in [11] go back essentially to Hardy-Littlewood [5], Hardy [4], Hecke [6], Wilton [19] and Walfisz [18].

Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 150 - 158
Copyright
Copyright © University College London 1984

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