Results 1 to 10 of about 56 (55)

AVERAGES OF EXPONENTIAL TWISTS OF THE VON MANGOLDT FUNCTION

Bulletin of the Australian Mathematical Society, 2022
AbstractWe obtain some improved results for the exponential sum $\sum _{x<n\leq 2x}\Lambda (n)e(\alpha k n^{\theta })$ with $\theta \in (0,5/12),$ where $\Lambda (n)$ is the von Mangoldt function. Such exponential sums have relations with the so-called quasi-Riemann hypothesis and were considered by Murty and Srinivas [‘On the uniform ...
XIUMIN REN, WEI ZHANG
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Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions

Journal of the European Mathematical Society, 2023
We establish quantitative bounds on the U^{k}[N] Gowers norms of the Möbius function  \mu and the von Mangoldt function \Lambda for all k
Tao, Terence, Teräväinen, Joni
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POLYNOMIAL PATTERNS IN THE PRIMES

Forum of Mathematics, Pi, 2018
Let $P_{1},\ldots ,P_{k}:\mathbb{Z}\rightarrow \mathbb{Z}$ be polynomials of degree at most ...
TERENCE TAO, TAMAR ZIEGLER
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Sums of divisor functions and von Mangoldt convolutions in 𝔽 _q [T] leading to symplectic distributions

Forum Mathematicum, 2022
Abstract In [J. P. Keating, B. Rodgers, E. Roditty-Gershon and Z. Rudnick, Sums of divisor functions in 𝔽 q
Vivian Kuperberg, Matilde Lalín
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Power series with the von Mangoldt function

Functiones et Approximatio Commentarii Mathematici, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kunik, Matthias, Lucht, Lutz G
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Correlations of the von Mangoldt and higher divisor functions II: divisor correlations in short ranges [PDF]

Mathematische Annalen, 2019
46 pages; incorporated referee comments and corrected a few additional ...
Matomäki, Kaisa, RadziwiÅ‚Å‚, Maksym, Tao, Terence   +2 more
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Study of the generalized von mangoldt function defined by L-additive function

, 2023
14 ...
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Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges

Proceedings of the London Mathematical Society, 2018
80 pages, no figures.
Matomäki, Kaisa, Radziwiłł, Maksym, Tao, Terence   +2 more
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On Universality of Some Beurling Zeta-Functions

Axioms
Let P be the set of generalized prime numbers, and ζP(s), s=σ+it, denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζP(s+iτ), τ∈R. We assume the classical axioms for the
Andrius Geštautas, Antanas Laurinčikas
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The Riemann Hypothesis via the generalizedvon Mangoldt function

Functiones et Approximatio Commentarii Mathematici
Gonek, Graham, and Lee have shown recently that the Riemann Hypothesis (RH) can be reformulated in terms of certain asymptotic estimates for twisted sums with von Mangoldt function $Λ$. Building on their ideas, for each $k\in\mathbb{N}$, we study twisted sums with the \emph{generalized von Mangoldt function} $$ Λ_k(n):=\sum_{d\,\mid\,n}μ(d)\Big(\log ...
Banks, William, Sinha, Saloni
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