Lower bounds on odd order character sums

Details Lower bounds on odd order character sums Lower bounds on odd order character sums

2011-09-07

arxiv.org/abs/1109.1348v1

Mathematics

Number Theory

6 pages

Scientific paper

A classical result of Paley shows that there are infinitely many quadratic characters $\chi\mod{q}$ whose character sums get as large as $\sqrt{q}\log \log q$; this implies that a conditional upper bound of Montgomery and Vaughan cannot be improved. In this paper, we derive analogous lower bounds on character sums for characters of odd order, which are best possible in view of the corresponding conditional upper bounds recently obtained by the first author.

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