Results 171 to 180 of about 1,625,058 (297)
A few equalities involving integrals of the logarithm of the Riemann Zeta-function and equivalent to the Riemann hypothesis [PDF]
arXiv, 2008 Using a generalized Littlewood theorem concerning integrals of the logarithm of analytical functions, we have established a few equalities involving integrals of the logarithm of the Riemann Zeta-function and have rigorously proven that they are equivalent to the Riemann hypothesis.
arxiv
A Stratonovich integral for anticipating processes
Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7695-7705, 15 May 2025.A stochastic integral for anticipating integrands was introduced by Ayed and Kuo in 2008. Riemann–Stieltjes sums were considered, where the adapted part of the integrand was evaluated at the left endpoints of the subintervals, while the instantly independent part was evaluated at the right endpoints.
Marc Jornet
wiley +1 more source
On the Approximation of the Hardy Z-Function via High-Order Sections
AxiomsThe Z-function is the real function given by Z(t)=eiθ(t)ζ12+it, where ζ(s) is the Riemann zeta function, and θ(t) is the Riemann–Siegel theta function. The function, central to the study of the Riemann hypothesis (RH), has traditionally posed significant
Yochay Jerby
doaj +1 more source
Mathematische Nachrichten, Volume 298, Issue 5, Page 1617-1632, May 2025.Abstract Let h$h$ be a fixed non‐zero integer. For every t∈R+$t\in \mathbb {R}_+$ and every prime p$p$, consider the angles between rays from an observer located at the point (−tJp2,0)$(-tJ_p^2,0)$ on the real axis toward the set of all integral solutions (x,y)$(x,y)$ of the equation y−1−x−1≡hmodp$y^{-1}-x^{-1}\equiv h \left(\mathrm{ mod\;}p\right)$ in
Jack Anderson +3 more
wiley +1 more source
Jacobian elliptic fibrations on K3s with a non‐symplectic automorphism of order 3
Mathematische Nachrichten, Volume 298, Issue 5, Page 1758-1788, May 2025.Abstract Let X$X$ be a K3 surface admitting a non‐symplectic automorphism σ$\sigma$ of order 3. Building on work by Garbagnati and Salgado, we classify the Jacobian elliptic fibrations on X$X$ with respect to the action of σ$\sigma$ on their fibers. If the fiber class of a Jacobian elliptic fibration on NS(X)$\operatorname{NS}(X)$ is fixed by σ$\sigma$,
Felipe Zingali Meira
wiley +1 more source
An Equivalent to the Riemann Hypothesis
, 2023 The Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis.
openaire +1 more source
The Effect of the Density of Square-Free ωp-numbers on the Bounds of Beurling Counting Function
Zanco Journal of Pure and Applied SciencesPrimitive weird numbers are weird numbers which are not a multiple of any smaller weird numbers. The goal of this work is to use a square-free primitive weird number x=ab where b be an increasing sequence of prime numbers such that q1 is greater than ∏
Sarah Al-Ebrahimy, Eman F. Mohommed
doaj +1 more source
International Journal of Language &Communication Disorders, Volume 60, Issue 3, May/June 2025.ABSTRACT Background Content validity is a key measurement property that should be considered when selecting or reviewing a patient‐reported outcome measure (PROM). In the field of communication disorders, there are several PROMs available, most of which are disease specific.
Lizet Van Ewijk +3 more
wiley +1 more source
, 2012 This paper has been withdrawn by the author due to a crucial error on last page: The choice of the functions F and G does not meet condition 4 of Theorem ...
openaire +2 more sources
Euler–Riemann–Dirichlet Lattices: Applications of η(s) Function in Physics
MathematicsWe discuss applications of the Dirichlet η(s) function in physics. To this end, we provide an introductory description of one-dimensional (1D) ionic crystals, which are well-known in the condensed matter physics literature, to illustrate the central ...
Hector Eduardo Roman
doaj +1 more source