Results 21 to 30 of about 268 (51)
On Waring's problem for intermediate powers [PDF]
, 2016 Let $G(k)$ denote the least number $s$ such that every sufficiently large natural number is the sum of at most $s$ positive integral $k$th powers. We show that $G(7)\le 31$, $G(8)\le 39$, $G(9)\le 47$, $G(10)\le 55$, $G(11)\le 63$, $G(12)\le 72$, $G(13 ...
Wooley, Trevor D.
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The density of zeros of forms for which weak approximation fails [PDF]
, 1992 The weak approximation principal fails for the forms x3 + y3 + z3 = kw3, when k = 2 or 3. The question therefore arises as to what asymptotic density one should predict for the rational zeros of these forms.
Heath-Brown, D. R.
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On the Waring--Goldbach problem for eighth and higher powers [PDF]
, 2015 Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function $H(k)$ in the Waring--Goldbach problem.
Angel V. Kumchev, D. Wooley, Trevor
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Bihomogeneous forms in many variables [PDF]
, 2013 We count integer points on bihomogeneous varieties using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in using the ...
Schindler, Damaris
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Asymptotics for rank and crank moments
, 2009 Moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms.
Bringmann, K., Mahlburg, K., Rhoades, R.
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A Diophantine problem with prime variables [PDF]
, 2012 We study the distribution of the values of the form $\lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real number not all of the same sign, with $\lambda_1 / \lambda_2$ irrational, and $p_1 ...
Languasco, Alessandro +1 more
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An Invitation to Additive Prime Number Theory [PDF]
, 2005 2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number ...
Kumchev, A., Tolev, D.
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On Waring's problem: two squares, two cubes and two sixth powers [PDF]
, 2013 We investigate the number of representations of a large positive integer as the sum of two squares, two positive integral cubes, and two sixth powers, showing that the anticipated asymptotic formula fails for at most O((log X)^3) positive integers not ...
Wooley, Trevor D.
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On the saturation number for cubic surfaces
, 2014 We investigate the density of rational points on the Fermat cubic surface and the Cayley cubic surface whose coordinates have few prime factors. The key tools used are the weighted sieve, the circle method and universal torsors.Comment: 20 pages ...
Wang, Yuchao
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Sum of one prime and two squares of primes in short intervals [PDF]
, 2015 Assuming the Riemann Hypothesis we prove that the interval $[N, N + H]$ contains an integer which is a sum of a prime and two squares of primes provided that $H \ge C (\log N)^{4}$, where $C > 0$ is an effective constant.Comment: removed unconditional ...
Languasco, Alessandro +1 more
core +3 more sources