Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Adrian W. Dudek"'
Autor:
Michaela Cully-Hugill, Adrian W. Dudek
Publikováno v:
Research in Number Theory. 8
We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.
10 pages, comments welcome
10 pages, comments welcome
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::371fef29c6b218db23ce2c799b80f9fb
https://doi.org/10.1007/s40993-022-00358-1
https://doi.org/10.1007/s40993-022-00358-1
We prove explicit versions of Cram\'er's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
Comment: A misprint in a formula has been corrected; all constants appearing in the conclusions have
Comment: A misprint in a formula has been corrected; all constants appearing in the conclusions have
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b379f3bf843cee80d1ad10b45c751c3
http://hdl.handle.net/10446/140234
http://hdl.handle.net/10446/140234
Autor:
Adrian W. Dudek
Publikováno v:
Graphs and Combinatorics. 32:1843-1850
We show that the gap between the two greatest eigenvalues of the generalised Petersen graphs P(n, k) tends to zero as $$n \rightarrow \infty $$nźź. Moreover, we provide explicit upper bounds on the size of this gap. It follows that these graphs hav
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1861159e4a9a87df51371d45bd6bea36
https://doi.org/10.1007/s00373-016-1676-0
https://doi.org/10.1007/s00373-016-1676-0
Lapkova [‘On the average number of divisors of reducible quadratic polynomials’, J. Number Theory 180 (2017), 710–729] uses a Tauberian theorem to derive an asymptotic formula for the divisor sum $\sum _{n\leq x}d(n(n+v))$ where $v$ is a fixed
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f5e60ade1c2b7249f58f17caef80053
Autor:
Adrian W. Dudek
Publikováno v:
The Ramanujan Journal. 42:233-240
We prove that every integer greater than two may be written as the sum of a prime and a square-free number.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b03767ada20eb5d0a618737841debb3c
https://doi.org/10.1007/s11139-015-9736-2
https://doi.org/10.1007/s11139-015-9736-2
Autor:
David J. Platt, Adrian W. Dudek
Publikováno v:
Experimental Mathematics. 24:289-294
Ramanujan proved that the inequality holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp (9658). Furthermore, we solve the inequality c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c444f35eb850097ba62b5ab345b308e0
https://doi.org/10.1080/10586458.2014.990118
https://doi.org/10.1080/10586458.2014.990118
Autor:
Adrian W. Dudek
Publikováno v:
International Journal of Number Theory. 11:771-778
We prove some results concerning the distribution of primes assuming the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval [Formula: see text] for all x ≥ 2; this improves a result of Ramaré and Saou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f27e722f46e3f7e028ff1e45f6bb3ee6
https://doi.org/10.1142/s1793042115500426
https://doi.org/10.1142/s1793042115500426
Autor:
Adrian W. Dudek
Publikováno v:
European Journal of Combinatorics. 43:204-209
The method of Murty and Cioab? shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus eliminates th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9c98ff70b904635abf301b3211fa4bd4
https://doi.org/10.1016/j.ejc.2014.09.001
https://doi.org/10.1016/j.ejc.2014.09.001
Autor:
Adrian W. Dudek
Publikováno v:
Funct. Approx. Comment. Math. 55, no. 2 (2016), 177-197
We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.3))$. This is done by first deriving the Riemann--von Mangoldt explicit formula for the Riemann zeta-function with explicit bounds on the error term. We use this
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba8caf5e95c671093515aac8cce4198b
http://projecteuclid.org/euclid.facm/1481943881
http://projecteuclid.org/euclid.facm/1481943881
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
Comment: Corrected Corollary 4.1. Minor changes to the bibliography. To appear in Int. J. Number Theory
Comment: Corrected Corollary 4.1. Minor changes to the bibliography. To appear in Int. J. Number Theory
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf14592c8b0fbc23180a69c8a82a912a
http://hdl.handle.net/10446/58043
http://hdl.handle.net/10446/58043