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arXiv · 1109.1786

The resonance method for large character sums

Bob Hough
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Abstract

We consider the size of large character sums, proving new lower bounds for the quantity $Δ(N,q) = \sup_{χ\neq χ_0 mod q} |\sum_{n < N} χ(n)|$ for almost all ranges of $N$. The results are proven using the resonance method and saddle point analysis.

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Bob Hough. 2011-09-08. The resonance method for large character sums. https://doi.org/10.1112/s0025579312001015

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