Results 1 to 10 of about 1,625,058 (297)
The Riemann Zeros as Spectrum and the Riemann Hypothesis [PDF]
Symmetry, 2016 We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers.
G. Sierra
semanticscholar +7 more sources
Symmetries and the Riemann Hypothesis [PDF]
arXiv, 2008 Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann's zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis.
Lin Weng
arxiv +7 more sources
Black holes, quantum chaos, and the Riemann hypothesis [PDF]
SciPost Physics Core, 2021 Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for
Panagiotis Betzios, Nava Gaddam, Olga Papadoulaki
doaj +2 more sources
Riemann hypothesis for period polynomials of modular forms. [PDF]
Proc Natl Acad Sci U S A, 2016 Significance Critical values of modular L-functions are objects of central importance in arithmetic geometry and number theory. These numbers are predicted to encode deep arithmetic information by the Birch and Swinnerton-Dyer conjecture and the Bloch ...
Jin S, Ma W, Ono K, Soundararajan K.
europepmc +3 more sources
New versions of the Nyman-Beurling criterion for the Riemann hypothesis [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Let ρ(x)=x−[x], χ=χ(0,1), λ(x)=χ(x)logx, and M(x)=ΣK≤x μ(k), where μ is the Möbius function.
Luis Báez-Duarte
doaj +2 more sources
Large gaps between consecutive zeros of the Riemann zeta-function. II [PDF]
arXiv, 2013 Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.
Bui, H. M.
arxiv +3 more sources
Variants on Andrica’s Conjecture with and without the Riemann Hypothesis [PDF]
Mathematics, 2018 The gap between what we can explicitly prove regarding the distribution of primes and what we suspect regarding the distribution of primes is enormous. It is (reasonably) well-known that the Riemann hypothesis is not sufficient to prove Andrica’s ...
Matt Visser
doaj +2 more sources
Colloquium: Physics of the Riemann hypothesis [PDF]
, 2011 Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics.
Dániel Schumayer, D. A. W. Hutchinson
openalex +3 more sources
One page proof of the Riemann hypothesis [PDF]
arXiv, 2007 We give a short Wiener measure proof of the Riemann hypothesis based on a surprising, unexpected and deep relation between the Riemann zeta $\zeta(s)$ and the trivial zeta $\zeta_{t}(s):=Im(s)(2Re(s)-1)$.
Andrzej Mądrecki
arxiv +3 more sources
Chebyshev's bias and generalized Riemann hypothesis [PDF]
, 2011 It is well known that $li(x)>\pi(x)$ (i) up to the (very large) Skewes' number $x_1 \sim 1.40 \times 10^{316}$ \cite{Bays00}. But, according to a Littlewood's theorem, there exist infinitely many $x$ that violate the inequality, due to the specific ...
Adel Alahmadi +2 more
openalex +6 more sources