Large Character Sums: Burgess’s Theorem and Zeros of L-functions
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چکیده
We study the conjecture that ∑ n≤x χ(n) = o(x) for any primitive Dirichlet character χ (mod q) with x ≥ q , which is known to be true if the Riemann Hypothesis holds for L(s, χ). We show that it holds under the weaker assumption that ‘100%’ of the zeros of L(s, χ) up to height 14 lie on the critical line. We also establish various other consequences of having large character sums; for example, that if the conjecture holds for χ then it also holds for χ.
منابع مشابه
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تاریخ انتشار 2015