Results 1 to 10 of about 26,193 (79)
The inverses of tails of the Riemann zeta function [PDF]
Journal of Inequalities and Applications, 2018 We present some bounds of the inverses of tails of the Riemann zeta function on $0 < s < 1$ and compute the integer parts of the inverses of tails of the Riemann zeta function for $s=\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$.Comment: 12 ...
Kim, Donggyun, Song, Kyunghwan
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Amplitudes and the Riemann Zeta Function [PDF]
Physical Review Letters, 2021 Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses $m_n^2 = _n^2$, where $ \left(\frac{1}{2} \pm i _n\right) = 0$.
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Pseudomoments of the Riemann zeta function [PDF]
Bulletin of the London Mathematical Society, 2018 The $2$kth pseudomoments of the Riemann zeta function $ (s)$ are, following Conrey and Gamburd, the $2k$th integral moments of the partial sums of $ (s)$ on the critical line. For fixed $k>1/2$, these moments are known to grow like $(\log N)^{k^2}$, where $N$ is the length of the partial sum, but the true order of magnitude remains unknown when $k\
Bondarenko, Andriy +4 more
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Riemann’s zeta function and beyond [PDF]
Bulletin of the American Mathematical Society, 2003 In recent yearsLL-functions and their analytic properties have assumed a central role in number theory and automorphic forms. In this expository article, we describe the two major methods for proving the analytic continuation and functional equations ofLL-functions: the method of integral representations, and the method of Fourier expansions of ...
Stephen Gelbart, Stephen D. Miller
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Quantization of the Riemann Zeta-Function and Cosmology [PDF]
, 2007 Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories.
Barnaby N. +18 more
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Quantum Spin Chains and Riemann Zeta Function with Odd Arguments [PDF]
, 2001 Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model.
Berruto F +23 more
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On the mod-Gaussian convergence of a sum over primes [PDF]
, 2013 We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $\operatorname{Im}\log\zeta(1/2+it)$. This Dirichlet polynomial is sufficiently long to deduce Selberg's central limit theorem with an explicit error term. Moreover, assuming
Wahl, Martin
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Operator-valued zeta functions and Fourier analysis [PDF]
, 2019 The Riemann zeta function $\zeta(s)$ is defined as the infinite sum $\sum_{n=1}^\infty n^{-s}$, which converges when ${\rm Re}\,s>1$. The Riemann hypothesis asserts that the nontrivial zeros of $\zeta(s)$ lie on the line ${\rm Re}\,s= \frac{1}{2}$. Thus,
Bender, Carl M., Brody, Dorje C
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On the zeros of the Riemann zeta function
, 2021 Let Theta be the supremum of the real parts of the zeros of the Riemann zeta function. By manipulating the Dirichlet series for 1/zeta(s), we demonstrate that Theta=1. In particular, this disproves the Riemann hypothesis that Theta=1/2.
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Moments of the Riemann zeta function [PDF]
Annals of Mathematics, 2009 Assuming the Riemann Hypothesis we obtain an upper bound for the moments of the Riemann zeta-function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments. The method extends to moments in families of $L$-functions.
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