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Sharpenings of Li's Criterion for the Riemann Hypothesis

✍ Scribed by André Voros

Publisher
Springer Netherlands
Year
2006
Tongue
English
Weight
343 KB
Volume
9
Category
Article
ISSN
1385-0172

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📜 SIMILAR VOLUMES

Complements to Li's Criterion for the Ri
Complements to Li's Criterion for the Riemann Hypothesis
✍ Enrico Bombieri; Jeffrey C. Lagarias 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 131 KB

In a recent paper Xian-Jin Li showed that the Riemann Hypothesis holds if and only if \* n = \ [1&(1&1Â\) n ] has \* n >0 for n=1, 2, 3, ... where \ runs over the complex zeros of the Riemann zeta function. We show that Li's criterion follows as a consequence of a general set of inequalities for an

On Beurling′s Real Variable Reformulatio
On Beurling′s Real Variable Reformulation of the Riemann Hypothesis
✍ L Baezduarte 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 623 KB

Let \(\rho(x)\) be the fractional part of \(x, B\) is the linear space of functions \(\sum_{1 \leqslant k \leqslant n} a_{k} \rho\left(\theta_{k} / x\right), \theta_{k} \in(0,1], \sum a_{k} \theta_{k}=0, n\) any positive integer. For \(p \in(1,2]\) Beurling proved that \(\zeta(s) \neq 0\) in \(\math