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The graphs of exponential sums

Published online by Cambridge University Press:  26 February 2010

J. H. Loxton
J. H. Loxton
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales, Australia, 2033.
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Extract

In [3], D. H. Lehmer has analysed the incomplete Gaussian sum

where N and q are positive integers with N < q and e(x) is an abbreviation for e2πix. The crucial observation is that, for almost all values of N, Gq(N) is in the vicinity of the point ¼(1 + i)q1/2. This leads to sharp estimates of the shape Gq(N) = O(q½).

Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 153 - 163
Copyright
Copyright © University College London 1983

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References

1.Jahnke, E. and Emde, F.. Tables of Junctions with formulae and curves (Dover, 1943).Google Scholar
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4.Loxlon, J. H.. Captain Cook and the Loch Ness monster. James Cook Mathematical Notes, 3 (1981), 3060–3064.Google Scholar
5.Rademacher, H.. Topics in analytic number theory (Springer, 1973).CrossRefGoogle Scholar