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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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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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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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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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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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Exponential Sums Over Primes in an Arithmetic Progression [PDF]
Proceedings of the American Mathematical Society, 1985 In 1979 A. F. Lavrik obtained some estimates for exponential sums over primes in arithmetic progressions by an analytic method. In the present paper we give an estimate for the same sums, comparable with Lavrik’s estimate, by means of elementary methods like Vaughan’s identity.
A. BALOG, PERELLI, ALBERTO
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Repairing Reed-Solomon Codes Over Prime Fields via Exponential Sums
IEEE Transactions on Information Theory, 2023 This paper presents two repair schemes for low-rate Reed-Solomon (RS) codes over prime fields that can repair any node by downloading a constant number of bits from each surviving node. The total bandwidth resulting from these schemes is greater than that incurred during trivial repair; however, this is particularly relevant in the context of leakage ...
Roni Con +3 more
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On certain exponential sums over primes
Journal of Number Theory, 2009 Let \(f(x)\) be a real valued polynomial of degree \(k\geq 4\) and irrational leading coefficient \(\alpha\). Exponential sums of the form \[ S:=\sum_{p\leq N} (\log p) e(f(p)) \] have received a lot of interest. \textit{G. Harman} proved in [Mathematika 28, 249--254 (1981; Zbl 0465.10029)] that if \(q\) is the denominator of a convergent of \(\alpha\),
Maier, H., Sankaranarayanan, A.
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Explicit upper bounds for exponential sums over primes [PDF]
Mathematics of Computation, 2000 We give explicit upper bounds for linear trigonometric sums over primes.
Daboussi, Hedi, Rivat, Joel
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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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