Results 1 to 10 of about 52 (51)
The inverses of tails of the Riemann zeta function [PDF]
Journal of Inequalities and Applications, 2018 We present some bounds of the inverses of tails of the Riemann zeta function on ...
Donggyun Kim, Kyunghwan Song
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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
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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
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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
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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
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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
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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
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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
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Estimates of convolutions of certain number‐theoretic error terms
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 1, Page 1-23, 2004., 2004 Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number‐theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the ...
Aleksandar Ivić
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Consecutive evaluation of Euler sums
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 9, Page 555-561, 2002., 2002 We describe a simple method for a consecutive evaluation of the Euler sums S(r, p), r = 1, 2, … in terms of zeta values.
Khristo N. Boyadzhiev
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