Results 111 to 120 of about 640,811 (318)

A Simple Proof Of The Prime Number Theorem [PDF]

arXiv, 2015
It is shown that the Mean Value Theorem for arithmetic functions, and simple properties of the zeta function are sufficient to assemble proofs of the Prime Number Theorem, and Dirichlet Theorem. These are among the simplest proofs of the asymptotic formulas of the corresponding prime counting functions.
arxiv  

From $p$-Adic to Zeta Strings [PDF]

arXiv, 2020
This article is related to construction of zeta strings from $p$-adic ones. In addition to investigation of $p$-adic string for a particular prime number $p$, it is also interesting to study collective effects taking into account all primes $p$. An idea behind this approach is that a zeta string is a whole thing with infinitely many faces which we see ...
arxiv  

A New Closed Formula for the Riemann Zeta Function at Prime Numbers

, 2023
The Riemann zeta function is one of the most important functions in mathematics, but it is also one of the most difficult to compute. In this paper, we present a new closed formula for the Riemann zeta function at prime numbers.
openaire   +1 more source

Enhancing CoFe Catalysts with V2CTX MXene‐Derived Materials for Anion Exchange Membrane Electrolyzers

Advanced Functional Materials, EarlyView.
MXene dervied CoFe composites show increased initial Oxygen Evolution Reaction (OER) activity compared to the pure CoFe and MXene in an Anion Exchange Membrane device. Vanadium vacancies in the MXene plays a role in increased OER activity and hinders Fe leaching in the AEM device over using the pure V2C MXene as a support material for the CoFe ...
Can Kaplan, Karuppasamy Dharmaraj, Thorsten Schultz, Leiqiang Qin, Ningjun Chen, Danielle A. Douglas‐Henry, Bastian Schmiedecke, Merve Buldu‐Akturk, Axel Zuber, Iris Dorbandt, Maximilian Reinhardt, Yael Rodriguez‐Ayllon, Yan Lu, Valeria Nicolosi, Norbert Koch, Johanna Rosen, Michelle P. Browne   +16 more
wiley   +1 more source

Unravelling quiescent optical solitons: An exploration of the complex Ginzburg–Landau equation with nonlinear chromatic dispersion and self-phase modulation

Nonlinear Engineering
In this investigation, we delve into the recovery of quiescent optical solitons amidst the onset of nonlinear chromatic dispersion (CD), employing the complex Ginzburg–Landau equation. Quiescent optical solitons, self-sustaining, locally distributed wave
Chou Dean, Amer Aamna, Rehman Hamood Ur, Li Ming-Lung   +3 more
doaj   +1 more source

Unicity Results Concerning of difference monomials of L-function and a meromorphic function

Ratio Mathematica
In this paper, we study the value distribution of $\mathcal{L}$-function in the extend Selberg class and a non-constant transcendental meromorphic $\mathsf{f}$ function with finitely many zeros of finite order, sharing a polynomial with its difference ...
Harina Waghamore P, Roopa M.
doaj   +1 more source

The $n$th+1 Prime Number Limit Formulas [PDF]

arXiv, 2016
A new derivation of Golomb's limit formula for generating the $n$th$+1$ prime number is presented. The limit formula is derived by extracting $p_{n+1}$ from Euler's prime product representation of the Riemann zeta function $\zeta(s)$ in the limit as $s$ approaches infinity.
arxiv  

A Non-Sieving Application of the Euler Zeta Function

, 2016
One familiar with the Euler zeta function, which established the remarkable relationship between the prime and composite numbers, might naturally ponder the results of the application of this special function in cases where there is no known way to sieve
May, Michael P.
core  

Magnetically Guided Mechanoactive Mineralization Scaffolds for Enhanced Bone Regeneration

Advanced Functional Materials, EarlyView.
A 3D‐printed ‘rebar‐concrete’ inspired scaffold (PGS‐P@MGel) synergizes spontaneous biomineralization with magneto‐mechanical stimulation through PDA@Fe3O4‐embedded hydrogel. This dual biointerface activates Piezo1/β‐catenin/YAP mechanotransduction axis, enhancing BMSCs osteogenesis and angiogenesis simultaneously.
Xuran Guo, Zaijin Tao, Zhenzhen Dai, Yinghua Gao, Chengzhen Chu, Cunyi Fan, Shen Liu, Xin Ma, Fangchun Jin, Zhengwei You, Jia Jiang   +10 more
wiley   +1 more source

Experiments with zeta zeros and Perron's formula [PDF]

arXiv, 2011
Of what use are the zeros of the Riemann zeta function? We can use sums involving zeta zeros to count the primes up to $x$. Perron's formula leads to sums over zeta zeros that can count the squarefree integers up to $x$, or tally Euler's $\phi$ function and other arithmetical functions. This is largely a presentation of experimental results.
arxiv