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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
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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
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The Bombieri–Vinogradov theorem for exponential sums over primes [PDF]
Notes on Number Theory and Discrete MathematicsIn 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
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SUMS OF KLOOSTERMAN SUMS OVER PRIMES IN AN ARITHMETIC PROGRESSION [PDF]
The Quarterly Journal of Mathematics, 2019 19 pages.
Dunn, Alexander, Zaharescu, Alexandru
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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.
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Exponential sum estimates over prime fields [PDF]
International Journal of Number Theory, 2019 In this paper, we prove some extensions of recent results given by Shkredov and Shparlinski on multiple character sums for some general families of polynomials over prime fields. The energies of polynomials in two and three variables are our main ingredients.
Koh, Doowon +3 more
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, 2021 Abstract In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers Hn(p,r,2,1) and Hn(p,r,2,1). Analogous results for numbers with k-prime factors will also be considered.
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On exponential sums over prime numbers [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989 AbstractIn this article we establish an estimate for a sum over primes that is the analogue of an estimate for a sum over consecutive integers which has proved to be very useful in applications of exponential sums to problems in number theory.
Sárközy, A., Stewart, C. L.
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Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem
Open Mathematics, 2017 In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., N=p13+…+pj3$\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with |pi−(N ...
Feng Zhao
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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.
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