Zobrazeno 1 - 10
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pro vyhledávání: '"Harman, Glyn"'
Autor:
Baker, Roger, Harman, Glyn
Let c > 0.55. Every large n can be written in the form p +ab, where p is prime, a and b are significantly smaller than x^1/2 and ab is less than n^c. This strengthens a result of Heath-Brown, which has the requirement c>3/4. We introduce the idea of
Externí odkaz:
http://arxiv.org/abs/2011.10859
Akademický článek
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Autor:
Harman, Glyn, Shparlinski, Igor E.
We show that for any $\varepsilon > 0$ and a sufficiently large cube-free $q$, any reduced residue class modulo $q$ can be represented as a product of $14$ integers from the interval $[1, q^{1/4e^{1/2} + \varepsilon}]$. The length of the interval is
Externí odkaz:
http://arxiv.org/abs/1408.4515
This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/1201.1210
Autor:
Harman, Glyn, Kumchev, Angel
Publikováno v:
J. Number Theory 130 (2010), 1969-2002
In this paper we continue our study, begun in part I, of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious oversight in ou
Externí odkaz:
http://arxiv.org/abs/0902.4190
Autor:
Everest, Graham, Harman, Glyn
We study primitive divisors of terms of the sequence P_n=n^2+b, for a fixed integer b which is not a negative square. It seems likely that the number of terms with a primitive divisor has a natural density. This seems to be a difficult problem. We su
Externí odkaz:
http://arxiv.org/abs/math/0701234
Autor:
Harman, Glyn, Wong, Kam C.
Publikováno v:
The American Mathematical Monthly, 2000 Nov 01. 107(9), 834-837.
Externí odkaz:
https://www.jstor.org/stable/2695739
Autor:
Harman, Glyn
In the first part of this thesis various problems in diophantine approximation are considered, which generalize well known theorems of Dirichlet and Kronecker. A brief survey is presented in the first chapter, including a discussion on the scope of e
Externí odkaz:
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.704506
Autor:
Harman, Glyn, Kumchev, Angel
Publikováno v:
In Journal of Number Theory 2010 130(9):1969-2002
Autor:
HARMAN, Glyn
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2003 Jan 01. 15(3), 727-740.
Externí odkaz:
https://www.jstor.org/stable/43974284