Results 41 to 50 of about 2,061 (84)
Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$
Proceedings of the London Mathematical Society, Volume 128, Issue 3, March 2024.Abstract We obtain the exponent of distribution 1/2+1/30$1/2+1/30$ for the ternary divisor function d3$d_3$ to square‐free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath‐Brown and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with GL(2)$GL(2)$ coefficients obtained using the delta ...
Prahlad Sharma
wiley +1 more source
Note on the Theory of Correlation Functions
, 2019 The purpose of this note is to improve the current theoretical results for the correlation functions of the Mobius sequence $\{\mu(n): n\geq 1 \}$ and the Liouville sequence $\{\lambda(n): n\geq 1 \}$.Comment: Sixty Six Pages.
Carella, N. A.
core
The master function and applications
, 2018 In this paper we introduce a function that is neither additive nor multiplicative, and is somewhat akin to the Von Mangoldt function. As an application we show that \begin{align}\sum \limits_{p\leq x/2}\frac{\pi(p)}{p}\geq (1+o(1))\log \log x\nonumber ...
Agama, Theophilus
core
A remark on the strong Goldbach conjecture
, 2018 Under the assumption that $\sum \limits_{n\leq N}\Upsilon(n)\Upsilon(N-n)>0$, we show that for all even number $N>6$ \begin{align} \sum \limits_{n\leq N}\Upsilon(n)\Upsilon(N-n)=(1+o(1))K\sum \limits_{p|N}\sum \limits_{\substack{n\leq N/p}}\Lambda_{0}(n)\
Agama, Theophilus
core
The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-function
, 2016 The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function.
Zaccagnini, Alessandro
core
A logarithmic improvement in the Bombieri-Vinogradov theorem
, 2017 In this paper we improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)^2 instead of (log x)^(5/2). We use a weighted form of Vaughan's identity, allowing a smooth truncation inside the procedure, and an estimate due to Barban ...
Sedunova, Alisa
core
Riemann's Zeta Function and Prime Numbers : an approximation using von Mangoldt's explicit formula
, 2023 This essay aims to explain the connection between Riemann's zeta function and prime numbers. It relies heavily on Riemann's 1859 manuscript, in which he approximates the prime-counting function using the non-trivial zeros of the zeta function. The main result of this essay is von Mangoldt's explicit formula, which is a modified version of Riemann's ...
openaire +1 more source
From Grafts to Human Bioengineered Vascularized Skin Substitutes. [PDF]
Int J Mol Sci, 2020 Oualla-Bachiri W +3 more
europepmc +1 more source
Liouville function, von Mangoldt function and norm forms at random binary forms
39 ...
openaire +2 more sources
Pair correlation and twin primes revisited. [PDF]
Proc Math Phys Eng Sci, 2016 Conrey B, Keating JP.
europepmc +1 more source