Results 11 to 20 of about 24,999 (231)
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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Brun's Fundamental Lemma and Exponential Sums over Primes
Journal of Number Theory, 2001 Using only a fundamental lemma in sieve methods together with Chebyshev's estimate for the average value for the von Mangoldt function \(\Lambda(n)\), the author establishes the bound for the exponential sum \[ \sum_{n\leq x}\Lambda(n)e^{2\pi i\alpha n}\ll x \sqrt{{d(q)\log^3q\over \varphi(q)}}, \] where \(d(q)\) is the divisor function and \(\varphi(q)
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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.
Huang, Bingrong, Wang, Zhiwei
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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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Restriction theory of the Selberg sieve, with applications [PDF]
, 2004 The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an L^2-L^p restriction theorem for majorants of this type.
Green, Ben, Tao, Terence
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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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