On Short Sums Of Trace Functions

We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging the "Polya-Vinogradov gap" in some sense) for bounded functions with bounded Fourier transforms. We then prove that the existence of non-trivial estimates for ranges slightly below the square-root bound is stable under the discrete Fourier transform. We then give applications related to trace functions over finite fields.


Published in:
Annales De L Institut Fourier, 67, 1, 423-449
Year:
2017
Publisher:
St Martin D Heres Cedex, Annales Inst Fourier
ISSN:
0373-0956
Keywords:
Laboratories:




 Record created 2017-03-27, last modified 2018-09-13


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