Sharpenings of Li's Criterion for the Riemann Hypothesis

被引：0
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作者：
André Voros
机构：
[1] CEA,
[2] Service de Physique Théorique de Saclay,undefined
[3] (CNRS URA 2306),undefined
来源：
Mathematical Physics, Analysis and Geometry | 2006年 / 9卷
关键词：
Riemann zeta function; Riemann hypothesis; Li's criterion; saddle-point method; Stieltjes constants; 11M26; 30B40; 41A60;
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学科分类号：
摘要：
Exact and asymptotic formulae are displayed for the coefficients λn used in Li's criterion for the Riemann Hypothesis. For n → ∞ we obtain that if (and only if) the Hypothesis is true, λn ∼ n(A log n + B) (with A > 0 and B explicitly given, also for the case of more general zeta or L-functions); whereas in the opposite case, λn has a non-tempered oscillatory form.
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页码：53 / 63
页数：10
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