Výsledky vyhledávání - "Primary 11M06, Secondary 11M26"

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Equivalent criteria for the Riemann hypothesis for a general class of $L$-functions

In 1916, Riesz gave an equivalent criterion for the Riemann hypothesis (RH). Inspired from Riesz's criterion, Hardy and Littlewood showed that RH is equivalent to the following bound: \begin{align*} P_1(x):= \sum_{n=1}^\infty \frac{\mu(n)}{n} \exp\le

Externí odkaz: http://arxiv.org/abs/2409.17708

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The sixth moment of Dirichlet L-functions at the central point

Autor: Chandee, Vorrapan, Li, Xiannan, Matomäki, Kaisa, Radziwiłł, Maksym

In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$-functions at the central point, averaged over primitive characters $\chi$ modulo $q$ and all moduli $q \leq Q$. In 2007, as an application of their ``asymptotic large

Externí odkaz: http://arxiv.org/abs/2409.01457

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Riesz type criteria for $L$-functions in the Selberg class

Autor: Gupta, Shivajee, Vatwani, Akshaa

We formulate a generalization of Riesz-type criteria in the setting of $L$-functions belonging to the Selberg class. We obtain a criterion which is sufficient for the Grand Riemann Hypothesis (GRH) for $L$-functions satisfying axioms of the Selberg c

Externí odkaz: http://arxiv.org/abs/2211.02954

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A weighted one-level density of the non-trivial zeros of the Riemann zeta-function

Autor: Bettin, Sandro, Fazzari, Alessandro

We compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by $|\zeta(\frac12+it)|^{2k}$ for $k=1$ and, for test functions with Fourier support in $(-\frac12,\frac12)$, for $k=2$. As a consequence, for $k=1,2$, we

Externí odkaz: http://arxiv.org/abs/2208.08421

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Riesz-type criteria for the Riemann hypothesis

Autor: Agarwal, Archit, Garg, Meghali, Maji, Bibekananda

Publikováno v: Proc. Amer. Math. Soc., 2022

In 1916, Riesz proved that the Riemann hypothesis is equivalent to the bound $\sum_{n=1}^\infty \frac{\mu(n)}{n^2} \exp\left( - \frac{x}{n^2} \right) = O_{\epsilon} \left( x^{-\frac{3}{4} + \epsilon} \right)$, as $x \rightarrow\infty$, for any $\epsi

Externí odkaz: http://arxiv.org/abs/2202.00637

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