Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Alexei Kourbatov"'
Autor:
Alexei Kourbatov, Marek Wolf
Publikováno v:
Mathematics, Vol 7, Iss 5, p 400 (2019)
Let q > r ≥ 1 be coprime integers. Let P c = P c ( q , r , H ) be an increasing sequence of primes p satisfying two conditions: (i) p ≡ r (mod q) and (ii) p starts a prime k-tuple with a given pattern H. Let π c ( x ) be the number of primes in
Externí odkaz:
https://doaj.org/article/7fa146c204554937ba41a1995021ab71
Autor:
Alexei Kourbatov
Publikováno v:
International Mathematical Forum. 13:65-78
Let $q>r\ge1$ be coprime integers. Let $R(n,q,r)$ be the $n$th record gap between primes in the arithmetic progression $r$, $r+q$, $r+2q,\ldots,$ and denote by $N_{q,r}(x)$ the number of such records observed below $x$. For $x\to\infty$, we heuristic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6739481a406328fa14f401b006f814d7
https://doi.org/10.12988/imf.2018.712103
https://doi.org/10.12988/imf.2018.712103
Autor:
Alexei Kourbatov
Publikováno v:
Alexei Kourbatov
We study two kinds of conjectural bounds for the prime gap after the k-th prime $p_k$: (A) $p_{k+1} < (p_k)^{1+1/k}$ and (B) $p_{k+1}-p_k < \log^2 p_k - \log p_k - b$ for $k>9$. The upper bound (A) is equivalent to Firoozbakht's conjecture. We prove
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df47c60eea073fa676b37b35173cb9bd
http://arxiv.org/abs/1506.03042
http://arxiv.org/abs/1506.03042
Autor:
Alexei Kourbatov
Publikováno v:
Alexei Kourbatov
Scopus-Elsevier
Scopus-Elsevier
Combining the Hardy-Littlewood k-tuple conjecture with a heuristic application of extreme-value statistics, we propose a family of estimator formulas for predicting maximal gaps between prime k-tuples. Computations show that the estimator a(log(x/a)-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d2180570f9ed81456a4b8283204a64d
http://arxiv.org/abs/1301.2242
http://arxiv.org/abs/1301.2242
Autor:
Alexei Kourbatov
In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between Cramer's r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d235d21b26f2f17132f4ee3ee5799d1
http://arxiv.org/abs/1401.6959
http://arxiv.org/abs/1401.6959
Autor:
Visser, Matt1 (AUTHOR) matt.visser@sms.vuw.ac.nz
Publikováno v:
Mathematics (2227-7390). Aug2019, Vol. 7 Issue 8, p691-691. 1p.
Autor:
Kourbatov, Alexei1 (AUTHOR) akourbatov@gmail.com, Wolf, Marek2 (AUTHOR) akourbatov@gmail.com
Publikováno v:
Mathematics (2227-7390). May2019, Vol. 7 Issue 5, p400. 1p.
Autor:
Giorgio Balzarotti, Paolo Pietro Lava
Problemi e congetture sfidanti per appassionati di calcoli e teoremi per verificare il grado delle proprie conoscenze e abilità matematiche. Il libro propone una serie di giochi in cui cimentarsi, per misurare la propria capacità di sciogliere ques
Autor:
Dominique De Nievre
L'histoire de la première des familles portant le nom'Evréinov'serait ordinaire si elle n'était pas frappée du sceau de l'originalité, par une origine spécifique : juive et marchande. Cette famille traverse en Russie tous les statuts sociaux. C