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A mean value theorem for exponential sums

Part of: Exponential sums and character sums

Published online by Cambridge University Press:  09 April 2009

M. N. Huxley
M. N. Huxley
Affiliation:
School of MathematicsUniversity of Wales College of Cardiff23 Senghenydd Road Cardiff, Wales CF2 4YH, UK
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Abstract

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The exponential sum S(x) = Σe(f(m + x)) has mean square size O(M), when m runs through M consecutive integers, f(x) satisfies bounds on the second and third derivatives, and x runs from 0 to 1.

MSC classification

Secondary: 11L07: Estimates on exponential sums
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 304 - 307
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Montgomery, H. L. and Vaughan, R. C., ‘Hilbert's inequality’, J. London Math. Soc. (2) 8 (1974), 73–82.CrossRefGoogle Scholar
[2]Graham, S. W. and Kolesnik, G., Van der Corput's method of exponential sums, London Math. Soc. Lecture Note Ser. 126 (Cambridge Univ. Press, Cambridge, 1991).CrossRefGoogle Scholar