Results 11 to 20 of about 59 (55)
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 ...
Kim D, Song K.
europepmc +2 more sources
Large oscillations of the argument of the Riemann zeta‐function
Bulletin of the London Mathematical Society, Volume 53, Issue 6, Page 1776-1785, December 2021., 2021 Abstract Let S(t) denote the argument of the Riemann zeta‐function, defined as S(t)=1πImlogζ(1/2+it).Assuming the Riemann hypothesis, we prove that S(t)=Ω±logtlogloglogtloglogt.This improves the classical Ω‐results of Montgomery (Theorem 2; Comment. Math. Helv. 52 (1977) 511–518) and matches with the Ω‐result obtained by Bondarenko and Seip (Theorem 2;
Andrés Chirre, Kamalakshya Mahatab
wiley +1 more source
Journal of the London Mathematical Society, Volume 103, Issue 4, Page 1618-1642, June 2021., 2021 Abstract We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object. Using these we determine the likely maximum of TlogT independently sampled copies of our sum and find that this is in agreement with a ...
Marco Aymone, Winston Heap, Jing Zhao
wiley +1 more source
Orthogonal forms: a simple tool for proving the irartionality of $\zeta (3)$ [PDF]
, 2009 33 pages, no figures.-- MSC2000 codes: Primary 42C05, 11B37, 11J72, 11M06; Secondary 30B70, 11A55, 11J70, 33C47.Submitted to: Journal of Approximation TheoryA new proof of the irrationality of $\zeta(3)$ is given. The orthogonality relation among certain
Arvesú Carballo, Jorge
core +3 more sources
Nonvanishing for cubic L-functions
Forum of Mathematics, Sigma, 2021 We prove that there is a positive proportion of L-functions associated to cubic characters over $\mathbb F_q[T]$ that do not vanish at the critical point $s=1/2$.
Chantal David +2 more
doaj +1 more source
THE DE BRUIJN–NEWMAN CONSTANT IS NON-NEGATIVE
Forum of Mathematics, Pi, 2020 For each $t\in \mathbb{R}$, we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where $\unicode[STIX]{x1D6F7}$ is the super-exponentially decaying function ...
BRAD RODGERS, TERENCE TAO
doaj +1 more source
Integer factoring and compositeness witnesses
Journal of Mathematical Cryptology, 2020 We describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x)M+O(1) to computing Euler’s totient function, with exceptions of at most xO(1/M) composite integers that cannot be factored at all, and at most x exp −cM ...
Pomykała Jacek, Radziejewski Maciej
doaj +1 more source
Average value of the divisor class numbers of real cubic function fields
Open Mathematics, 2023 We compute an asymptotic formula for the divisor class numbers of real cubic function fields Km=k(m3){K}_{m}=k\left(\sqrt[3]{m}), where Fq{{\mathbb{F}}}_{q} is a finite field with qq elements, q≡1(mod3)q\equiv 1\hspace{0.3em}\left(\mathrm{mod}\hspace{0 ...
Lee Yoonjin, Lee Jungyun, Yoo Jinjoo
doaj +1 more source
Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
Demonstratio Mathematica, 2023 In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
doaj +1 more source
Journal of Mathematical Cryptology, 2020 We introduce a new approach to (deterministic) integer factorisation, which could be described in the cryptographically fashionable term of “factoring with hints”: we prove that, for any ϵ > 0, given the knowledge of the factorisations of O(N1/3+ϵ) terms
Sica Francesco
doaj +1 more source