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Exponential sums connected with Ramanujan's function τ(n)

Published online by Cambridge University Press:  26 February 2010

L. A. Parson  and
Mark Sheingorn
L. A. Parson
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, U.S.A.
Mark Sheingorn
Affiliation:
The Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.
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Extract

This paper contains estimates of several exponential sums involving Fourier coefficients of certain modular forms. Although the questions which we consider date back, in some cases, to the twenties, our motivation is modern. All of these sums are connected with one approach to the problem of calculating the norm of the Poincaré 0-operator. In this section we state our results (and their antecedents) and then describe their relevance to the θ-operator problem. For simplicity we state and prove all our results for the modular cusp form of weight six, the famous discriminant function

Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 270 - 277
Copyright
Copyright © University College London 1982

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References

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