Results 1 to 10 of about 2,341 (116)

Variants on Andrica’s Conjecture with and without the Riemann Hypothesis

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   +3 more sources

Remarks on the Connection of the Riemann Hypothesis to Self-Approximation

Computation
By the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function ζ(s) by shifts ζ(s+iτ).
Antanas Laurinčikas
doaj   +3 more sources

Riemann hypothesis for period polynomials of modular forms [PDF]

Proceedings of the National Academy of Sciences of the United States of America, 2016
Kannan Soundararajan, Ken Ono, Wenjun Ma   +2 more
exaly   +2 more sources

Two generalizations of Liouville λ function [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
We study the properties of two classes of functions λₖ and ~λₖ that generalize the Liouville λ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of λₖ and ...
André Pierro de Camargo
doaj   +1 more source

Black holes, quantum chaos, and the Riemann hypothesis

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   +1 more source

Riemann hypothesis and Zeta-Function

Bibechana, 2018
No abstract available.
Mani Raj Bhattrai
doaj   +3 more sources

An Analytical and Numerical Detour for the Riemann Hypothesis

Information, 2021
From the functional equation F(s)=F(1−s) of Riemann’s zeta function, this article gives new insight into Hadamard’s product formula. The function S1(s)=d(lnF(s))/ds and its family of associated Sm functions, expressed as a sum of rational fractions, are ...
Michel Riguidel
doaj   +1 more source

The Riemann hypothesis and tachyonic off-shell string scattering amplitudes

European Physical Journal C: Particles and Fields, 2022
The study of the $$\mathbf{4}$$ 4 -tachyon off-shell string scattering amplitude $$ A_4 (s, t, u) $$ A 4 ( s , t , u ) , based on Witten’s open string field theory, reveals the existence of poles in the s-channel and associated to a continuum of complex “
Carlos Castro Perelman
doaj   +1 more source

Toward the Unification of Physics and Number Theory [PDF]

Reports in Advances of Physical Sciences, 2019
This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure.
Klee Irwin
doaj   +1 more source

Supersymmetry and the Riemann zeros on the critical line

Physics Letters B, 2019
We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip ...
Ashok Das, Pushpa Kalauni
doaj   +1 more source