The resonance method for large character sums

Published 8 Sep 2011 in math.NT | (1109.1786v1)

Abstract: We consider the size of large character sums, proving new lower bounds for the quantity $\Delta(N,q) = \sup_{\chi\neq \chi_0 mod q} |\sum_{n < N} \chi(n)|$ for almost all ranges of $N$. The results are proven using the resonance method and saddle point analysis.

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Bob Hough

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