Results 11 to 20 of about 571 (219)
, 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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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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New proof and generalization of some results on translated sums over k-almost primes
Comptes Rendus. MathématiqueA sequence $\mathcal{A}$ of strictly positive integers is said to be primitive if none of its terms divides the others, Erdős conjectured that the sum $f(\mathcal{A},0)\le f(\mathbb{N}_{1},0),$ where $\mathbb{N}_{1}$ is the sequence of prime numbers and $
Laib, Ilias
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On Erdős sums of almost primes
Comptes Rendus. MathématiqueIn 1935, Erdős proved that the sums $f_k=\sum _n 1/(n\log n)$, over integers $n$ with exactly $k$ prime factors, are bounded by an absolute constant, and in 1993 Zhang proved that $f_k$ is maximized by the prime sum $f_1=\sum _p 1/(p\log p)$.
Gorodetsky, Ofir +2 more
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Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Background Establishing a comprehensive apheresis medicine program in a resource‐constrained setting presents significant structural, financial, and logistical challenges. Despite the growing clinical importance of apheresis services globally, published experience from sub‐Saharan Africa remains sparse.
Folasade Adelekan‐Popoola +4 more
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Sums of Dilates Over Groups of Prime Order
The American Mathematical MonthlyFor $p$ prime, $A \subseteq \mathbb{Z}/p\mathbb{Z}$ and $λ\in \mathbb{Z}$, the sum of dilates $A + λ\cdot A$ is defined by \[A + λ\cdot A = \{a + λa' : a, a' \in A\}.\] The basic problem on such sums of dilates asks for the minimum size of $|A + λ\cdot A|$ for given $λ$, $A$ of given density $α$, and $p$ tending to infinity. We investigate this problem
Conlon, D, Lim, J
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Real exponential sums over primes and prime gaps
, 2023 27 pages, submitted to Annals of ...
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Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Background Japan has one of the highest dialysis prevalence rates worldwide and a shrinking, aging population. Whether dialysis burden has entered a sustained post‐peak phase or whether recent declines partly reflect pandemic‐related disruptions remains uncertain.
Hatice Şahin +2 more
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