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    Kowalski, Emmanuel and Sawin, William F. 2016. Kloosterman paths and the shape of exponential sums. Compositio Mathematica, Vol. 152, Issue. 07, p. 1489.

    Chamizo, Fernando and Raboso, Dulcinea 2015. Van der Corput method and optical illusions. Indagationes Mathematicae, Vol. 26, Issue. 5, p. 723.

    Paris, R.B. 2009. The asymptotics of a new exponential sum. Journal of Computational and Applied Mathematics, Vol. 223, Issue. 1, p. 314.

    Paris, R.B. 2005. An asymptotic approximation for incomplete Gauss sums. Journal of Computational and Applied Mathematics, Vol. 180, Issue. 2, p. 461.

    Evans, Ronald Minei, Marvin and Yee, Bennet 2003. Incomplete higher-order Gauss sums. Journal of Mathematical Analysis and Applications, Vol. 281, Issue. 2, p. 454.

    Loxton, J. H. 1985. The distribution of exponential sums. Mathematika, Vol. 32, Issue. 01, p. 16.


The graphs of exponential sums

  • J. H. Loxton (a1)
  • DOI:
  • Published online: 01 February 2010

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).

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5.H. Rademacher . Topics in analytic number theory (Springer, 1973).

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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