Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Daniel A. Goldston"'
Autor:
Ade Irma Suriajaya, Daniel A. Goldston
Publikováno v:
Journal of Number Theory. 227:144-157
We show that the error term in the asymptotic formula for the Ces{\`a}ro mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures cannot be too small and oscillates.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a308f7f879e1c14ef64a3f078c76af84
https://doi.org/10.1016/j.jnt.2021.03.004
https://doi.org/10.1016/j.jnt.2021.03.004
Autor:
DANIEL A. GOLDSTON, ADE IRMA SURIAJAYA
Fujii obtained a formula for the average number of Goldbach representations with lower order terms expressed as a sum over the zeros of the Riemann zeta-function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an unconditiona
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c873a16d98b244f58de41b52763ad2f9
http://arxiv.org/abs/2110.14250
http://arxiv.org/abs/2110.14250
A positive integer is called an $E_j$-number if it is the product of $j$ distinct primes. We prove that there are infinitely many triples of $E_2$-numbers within a gap size of $32$ and infinitely many triples of $E_3$-numbers within a gap size of $15
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d987652b79509a55dd36b0008fda0f9
Autor:
Ade Irma Suriajaya, Daniel A. Goldston
We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4618a11752a5807d3d6439eb2c521ca4
http://arxiv.org/abs/2007.16099
http://arxiv.org/abs/2007.16099
Autor:
S. W. Graham, Daniel A. Goldston, Jordan Schettler, Apoorva Panidapu, János Pintz, C. Y. Yildirim
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erd\H{o}s-Mirksy conjecture which states that there are infinitely many positive integers $x$ such t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cf374520aa348c7a52adf4006f5fc3d
http://arxiv.org/abs/2003.03661
http://arxiv.org/abs/2003.03661
Publikováno v:
Springer Optimization and Its Applications ISBN: 9783030558567
A Prime Difference Champion (PDC) for primes up to x is defined to be any element of the set of one or more differences that occur most frequently among all positive differences between primes ≤ x. Assuming an appropriate form of the Hardy–Little
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::643f47cb5cc593b93ecdcef82137303b
https://doi.org/10.1007/978-3-030-55857-4_9
https://doi.org/10.1007/978-3-030-55857-4_9
Publikováno v:
Irregularities in the Distribution of Prime Numbers ISBN: 9783319927763
We survey some past conditional results on the distribution of large gaps between consecutive primes and examine how the Hardy–Littlewood prime k-tuples conjecture can be applied to this question.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5aaaf1cc18a6a2d209b35c1163349b87
https://doi.org/10.1007/978-3-319-92777-0_3
https://doi.org/10.1007/978-3-319-92777-0_3
Autor:
Daniel A. Goldston, Andrew Ledoan
Publikováno v:
Mathematika. 61:719-740
An integer $d$ is called a jumping champion for a given $x$ if $d$ is the most common gap between consecutive primes up to $x$. Occasionally several gaps are equally common. Hence, there can be more than one jumping champion for the same $x$. For the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08654c102edee65fa1eed047c44827e2
https://doi.org/10.1112/s0025579315000078
https://doi.org/10.1112/s0025579315000078
Autor:
Daniel A. Goldston
In additive prime number theory the starting point of many investigations is the generating function (1) S ( α ) = ∑ p ≤ N ( log p ) e ( p α ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203747018/b2afbe02-bf0
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ecd7ce7ffbaa01cecf4f3b575612a36d
https://doi.org/10.4324/9780203747018-13
https://doi.org/10.4324/9780203747018-13