Results 1 to 10 of about 571 (219)

ON WEYL SUMS OVER PRIMES IN SHORT INTERVALS [PDF]

Number Theory: Arithmetic in Shangri-La, 2013
The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.
Angel Kumchev
exaly   +3 more sources

Average bounds for Kloosterman sums over primes [PDF]

Functiones Et Approximatio, Commentarii Mathematici, 2014
We prove two estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker.
exaly   +4 more sources

On certain sums over primes and the Riesz function

Математичні Студії
We offer some comments on series involving the M$\ddot{o}$bius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by applying Riemann-Stieltjes integration.
Alexander Patkowski
doaj   +3 more sources

Exponential sums over primes in short intervals

Journal of Number Theory, 2015
Let Λ(n) be the von Mangoldt function, x real and 2 ≤ y ≤ x.
Bingrong Huang
exaly   +4 more sources

Translated sums of primitive sets

Comptes Rendus. Mathématique, 2022
The Erdős primitive set conjecture states that the sum $f(A) = \sum _{a\,\in \,A}\tfrac{1}{a\log a}$, ranging over any primitive set $A$ of positive integers, is maximized by the set of prime numbers.
Lichtman, Jared Duker
doaj   +1 more source

The Bombieri-Vinogradov theorem for nilsequences

Discrete Analysis, 2021
The Bombieri-Vinogradov theorem for nilsequences, Discrete Analysis 2021:21, 55 pp. The prime number theorem asserts that the density of the primes in the vicinity of a large integer $n$ is approximately $1/\log n$, or equivalently that the number of ...
Xuancheng Shao, Joni Teräväinen
doaj   +1 more source

SUMS OF KLOOSTERMAN SUMS OVER PRIMES IN AN ARITHMETIC PROGRESSION [PDF]

The Quarterly Journal of Mathematics, 2019
For $q$ prime, $X \geq 1$ and coprime $u,v \in \mathbb{N}$ we estimate the sums \begin{equation*} \sum_{\substack{p \leq X \substack p \equiv u \hspace{-0.25cm} \mod{v} p \text{ prime}}} \text{Kl}_2(p;q), \end{equation*} where $\text{Kl}_2(p;q)$ denotes a normalised Kloosterman sum with modulus $q$.
Dunn, Alexander, Zaharescu, Alexandru
openaire   +2 more sources

The Bombieri–Vinogradov theorem for exponential sums over primes [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we revisit Lemma 18 from [2], which concerns a Bombieri–Vinogradov type theorem for exponential sums over primes. We provide a corrected version of the lemma, clarify the original arguments, and address certain inaccuracies present in the ...
Stoyan Dimitrov
doaj   +1 more source

Trigonometric sums over primes II [PDF]

Glasgow Mathematical Journal, 1981
We write e(x) for e2πix, ∥x∥ for the distance of x from the nearest integer and use A ≫ B to mean |A|<c |B|, where c is a positive constant depending at most on k and e. The letter p always denotes a prime number; P2 represents a number with precisely two prime factors.
openaire   +3 more sources

Sums over Primes

, 2021
See the abstract in the attached pdf.
openaire   +2 more sources