Results 31 to 40 of about 268 (51)
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.
core +3 more sources
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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Ces\`aro average in short intervals for Goldbach numbers
, 2017 We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals.Comment: revised version; to appear in Proc ...
Languasco, Alessandro +1 more
core +1 more source
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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Sums of four prime cubes in short intervals
, 2018 We prove that a suitable asymptotic formula for the average number of representations of integers $n=p_{1}^{3}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}$, where $p_1,p_2,p_3,p_4$ are prime numbers, holds in intervals shorter than the the ones previously known ...
Languasco, Alessandro +1 more
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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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On generating functions in additive number theory, II: lower-order terms and applications to PDEs. [PDF]
Math Ann, 2021 Brandes J +4 more
europepmc +1 more source
On the infinite Borwein product raised to a positive real power. [PDF]
Ramanujan J, 2023 Schlosser MJ, Zhou NH.
europepmc +1 more source
The epidemiology of blood transfusion in hospitalized children: a national cross-sectional study in China. [PDF]
Transl Pediatr, 2021 Guo K +7 more
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Diophantine approximation with one prime, two squares of primes and one $k$-th power of a prime
, 2017 Let ...
Gambini, Alessandro
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