Results 1 to 10 of about 2,023 (53)

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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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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A Ces\`aro Average of Goldbach numbers [PDF]

, 2012
Let $\Lambda$ be the von Mangoldt function and $(r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2))$ be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer.
Languasco, Alessandro, Zaccagnini, Alessandro   +1 more
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Efficient prime counting and the Chebyshev primes [PDF]

, 2011
The function $\epsilon(x)=\mbox{li}(x)-\pi(x)$ is known to be positive up to the (very large) Skewes' number. Besides, according to Robin's work, the functions $\epsilon_{\theta}(x)=\mbox{li}[\theta(x)]-\pi(x)$ and $\epsilon_{\psi}(x)=\mbox{li}[\psi(x)]-\
Planat, Michel, Solé, Patrick
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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
openaire   +3 more sources