Results 21 to 30 of about 72,493 (237)
On the Order of Growth of Lerch Zeta Functions
Mathematics, 2023 We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞.
Jörn Steuding, Janyarak Tongsomporn
doaj +1 more source
Moments of the Riemann zeta function [PDF]
, 2006 Assuming the Riemann hypothesis, we obtain an upper bound for the moments of the Riemann zeta function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments.
K. Soundararajan
semanticscholar +1 more source
Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function. [PDF]
Journal of Chemical Theory and Computation, 2019 In this communication we demonstrate the effectiveness of the method of complete basis set (CBS) extrapolation of correlation energies based on the application of the Riemann zeta function.
M. Lesiuk, B. Jeziorski
semanticscholar +1 more source
Precalculated arrays-based algorithms for the calculation of the Riemann zeta-function
Vilnius University Open Series, 2022 In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method.
Lukas Kuzma +2 more
doaj +1 more source
Decoupling, exponential sums and the Riemann zeta function [PDF]
, 2014 We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H].
J. Bourgain
semanticscholar +1 more source
New Results Involving Riemann Zeta Function Using Its Distributional Representation
Fractal and Fractional, 2022 The relation of special functions with fractional integral transforms has a great influence on modern science and research. For example, an old special function, namely, the Mittag–Leffler function, became the queen of fractional calculus because its ...
Asifa Tassaddiq, Rekha Srivastava
doaj +1 more source
Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function [PDF]
Journal of the London Mathematical Society, 2020 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.
Marco Aymone, Winston Heap, J. Zhao
semanticscholar +1 more source
Operator-valued zeta functions and Fourier analysis [PDF]
, 2019 The Riemann zeta function $\zeta(s)$ is defined as the infinite sum $\sum_{n=1}^\infty n^{-s}$, which converges when ${\rm Re}\,s>1$. The Riemann hypothesis asserts that the nontrivial zeros of $\zeta(s)$ lie on the line ${\rm Re}\,s= \frac{1}{2}$. Thus,
Bender, Carl M., Brody, Dorje C
core +2 more sources
International Journal of Mathematics and Mathematical Sciences, 2004 We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)=∑n=1∞(qn(s−1)/[n]s ...
Taekyun Kim
doaj +1 more source
Fungsi Zeta Riemann Genap Menggunakan Bilangan Bernoulli
Desimal, 2019 In this article, we study about the value of Riemann Zeta Function for even numbers using Bernoulli number. First, we give some basic theory about Bernoulli number and Riemann Zeta function.
Ikhsan Maulidi +2 more
doaj +1 more source