Results 21 to 30 of about 275 (62)
The sum of divisors of a quadratic form
, 2014 We study the sum of divisors of the quadratic form $m_1^2+m_2^2+m_3^2$. Let $$S_3(X)=\sum_{1\le m_1,m_2,m_3\le X}\tau(m_1^2+m_2^2+m_3^2).$$ We obtain the asymptotic formula $$S_3(X)=C_1X^3\log X+ C_2X^3+O(X^2\log^7 X),$$ where $C_1,C_2$ are two constants.
Zhao, Lilu
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Mean value estimates for odd cubic Weyl sums [PDF]
, 2014 We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's ...
Wooley, Trevor D.
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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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Weyl's inequality and systems of forms
, 2014 By providing a variant of Weyl's inequality for general systems of forms we establish the Hardy-Littlewood asymptotic formula for the density of integer zeros of systems of quadratic or cubics forms under weaker rank conditions than previously known.
Dietmann, Rainer
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Averages of shifted convolutions of $d_3(n)$ [PDF]
, 2011 We investigate the first and second moments of shifted convolutions of the generalised divisor function $d_3(n)$.Comment: 22 ...
Baier, S. +3 more
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On a Diophantine problem with two primes and s powers of two
, 2009 We refine a recent result of Parsell on the values of the form $\lambda_1p_1 + \lambda_2p_2 + \mu_1 2^{m_1} + ...m + \mu_s 2^{m_s}, $ where $p_1,p_2$ are prime numbers, $m_1,...c, m_s$ are positive integers, $\lambda_1 / \lambda_2$ is negative and ...
Languasco, A., Zaccagnini, A.
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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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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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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 Weyl sums for smaller exponents [PDF]
, 2010 We present a hybrid approach to bounding exponential sums over kth powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents k of intermediate ...
D. Wooley, Kent D. Boklan, Trevor
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