Results 1 to 10 of about 29,410 (152)

The inverses of tails of the Riemann zeta function. [PDF]

J Inequal Appl, 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 D, Song K.
europepmc   +2 more sources

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
core   +2 more sources

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., Bogoliubov N. N., Calcagni G., Chandrasekharan K., Faddeev L. D., Hellegouarch Yves, Hormander L., I. V. VOLOVICH, I. YA. AREF'EVA, Koshelev A. S., Kozlov V. V., Maslov V. P., Rapoport M., Shubin M. A., Titchmarsh E. C., Vladimirov V. S., Volovich I. V., Ya. Aref'eva I., Ya. Aref'eva I.   +18 more
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On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

, 2013
Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero.
Bui, H. M., Lester, S. J., Milinovich, M. B.   +2 more
core   +1 more source

Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

, 2018
Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line.
A Auffinger, A Bovier, A Bovier, B Derrida, B Derrida, B Duplantier, CM Newman, CM Newman, CM Newman, D Schumayer, E Bolthausen, E Titchmarsh, F Ouimet, F Ouimet, K Soundararajan, LP Arguin, LP Arguin, LP Arguin, LP Arguin, LP Arguin, LP Arguin, M Biskup, M Radizwiłł, O Daviaud, P Bourgade, P Carmona, Y Saouter, YV Fyodorov   +27 more
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On the Density–Density Correlations of the Non‐Interacting Finite Temperature Electron Gas

Contributions to Plasma Physics, EarlyView.
ABSTRACT The density–density correlations of the non‐interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic ...
Panagiotis Tolias, Tobias Dornheim, Jan Vorberger   +2 more
wiley   +1 more source

Multiple finite Riemann zeta functions

, 2004
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the ...
Kimoto, K., Kurokawa, N., Matsumoto, S., Wakayama, M.   +3 more
core   +1 more source

Locally Adaptive Non‐Hydrostatic Shallow Water Extension for Moving Bottom‐Generated Waves

International Journal for Numerical Methods in Fluids, EarlyView.
This study proposes a locally adaptive non‐hydrostatic model, which is based on the non‐hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation, and applies it to wave propagation generated by a moving bottom. To obtain the locally adaptive model, we investigate several potential adaptivity criteria based on the ...
Kemal Firdaus, Jörn Behrens
wiley   +1 more source

A Derivation of π(n) Based on a Stability Analysis of the Riemann-Zeta Function [PDF]

, 2010
The prime-number counting function π(n), which is significant in the prime number theorem, is derived by analyzing the region of convergence of the real-part of the Riemann- Zeta function using the unilateral z-transform.
Haranas, Ioannis, Harney, Michael
core   +1 more source

Theta and Riemann xi function representations from harmonic oscillator eigensolutions

, 2006
From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A
Abramowitz, Andrews, Atakishiyeva, Bump, Bump, Cartier, Coffey, Coffey, Coffey, Dykman, Edwards, Freilikher, Gradshteyn, Horikis, Keating, Kostelecký, Kurlberg, Lambert, Lebedev, Mark W. Coffey, Mehta, Nieto, Nieto, Platzman, Titchmarsh, Weyl   +25 more
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