Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Voros, André"'
Autor:
Voros, André
Publikováno v:
2023 J. Phys. A: Math. Theor. 56 064001
We survey sum rules for spectral zeta functions of homogeneous 1D Schr\"odinger operators, that mainly result from the exact WKB method.
Comment: 14 pages, 1 figure, 4 tables. In honour of Prof. M.V. BERRY's 80-th birthday. V2: new eqs.(32), (33
Comment: 14 pages, 1 figure, 4 tables. In honour of Prof. M.V. BERRY's 80-th birthday. V2: new eqs.(32), (33
Externí odkaz:
http://arxiv.org/abs/2206.14482
Autor:
Voros, André
The Riemann Hypothesis (RH) - that all nonreal zeros of Riemann's zeta function shall have real part 1/2 - remains a major open problem. Its most concrete equivalent is that an infinite sequence of real numbers, the Keiper--Li constants, shall be eve
Externí odkaz:
http://arxiv.org/abs/2204.01036
Autor:
Voros, André
Publikováno v:
Exp. Math. online 17 Jul 2018, print vol. 29(4) (2020) p. 452-469
The Keiper--Li sequence $\{ \lambda_n \}$ is most sensitive to the Riemann Hypothesis asymptotically ($n \to \infty$), but highly elusive both analytically and numerically. We deform it to fully explicit sequences, simpler to analyze and to compute (
Externí odkaz:
http://arxiv.org/abs/1703.02844
Autor:
Voros, André
The Keiper/Li constants $\{\lambda_n\}_{n=1,2,\ldots}$ are asymptotically ($n \to \infty$) sensitive to the Riemann Hypothesis, but highly elusive analytically and difficult to compute numerically. We present quite explicit variant sequences that sta
Externí odkaz:
http://arxiv.org/abs/1602.03292
Autor:
Voros, André
Publikováno v:
RIMS K\^oky\^uroku Bessatsu B52 (2014) 147-164
We review generalized zeta functions built over the Riemann zeros (in short: "superzeta" functions). They are symmetric functions of the zeros that display a wealth of explicit properties, fully matching the much more elementary Hurwitz zeta function
Externí odkaz:
http://arxiv.org/abs/1403.4558
Autor:
Voros, André
Publikováno v:
J. Phys. A 45 374007 (2012)
We review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schr\"odinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual) vs "classi
Externí odkaz:
http://arxiv.org/abs/1202.3100
Autor:
Voros, André
Following earlier studies, several new features of singular perturbation theory for one-dimensional quantum anharmonic oscillators are computed by exact WKB analysis; former results are thus validated.
Comment: Latex 17 pages, 1 figure; conferen
Comment: Latex 17 pages, 1 figure; conferen
Externí odkaz:
http://arxiv.org/abs/math-ph/0603043
Autor:
Voros, André
Publikováno v:
Math. Phys. Anal. Geom. 9 (2006) 53-63
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and
Externí odkaz:
http://arxiv.org/abs/math/0506326
Autor:
Voros, André
Publikováno v:
RIMS K\^oky\^uroku 1424 (2005) 214-231
We review an exact WKB resolution method for the stationary 1D Schr\"odinger equation with a general polynomial potential. This contribution covers already published material: we supply a commented summary here, stressing a few aspects which were les
Externí odkaz:
http://arxiv.org/abs/math-ph/0412041
Autor:
Voros, André
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to \infty$ (
Externí odkaz:
http://arxiv.org/abs/math/0404213