Lower bounds on odd order character sums
L Goldmakher, Y Lamzouri - … Mathematics Research Notices, 2012 - ieeexplore.ieee.org
International Mathematics Research Notices, 2012•ieeexplore.ieee.org
A classical result of Paley shows that there are infinitely many quadratic characters χ (mod q)
whose character sums get as large as 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.
whose character sums get as large as 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.
A classical result of Paley shows that there are infinitely many quadratic characters χ(mod q) whose character sums get as large as ; 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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