Results 21 to 30 of about 188 (37)
On Comon's and Strassen's conjectures [PDF]
, 2018 Comon's conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen's conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition.
Casarotti, Alex +2 more
core +2 more sources
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
core +1 more source
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
core
Almost all primes have a multiple of small Hamming weight
, 2016 Recent results of Bourgain and Shparlinski imply that for almost all primes $p$ there is a multiple $mp$ that can be written in binary as $mp= 1+2^{m_1}+ \cdots +2^{m_k}, \quad 1\leq m_1 < \cdots < m_k,$ with $k=66$ or $k=16$, respectively. We show that $
Elsholtz, Christian
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
core +1 more source
It takes two (seconds): decreasing encoding time for two-choice functional near-infrared spectroscopy brain-computer interface communication. [PDF]
Neurophotonics, 2023 Vorreuther A +6 more
europepmc +1 more source
Applications of some exponential sums on prime powers: a survey
, 2016 A survey paper on some recent results on additive problems with prime ...
Languasco, Alessandro
core
Restriction estimates of ε -removal type for k-th powers and paraboloids. [PDF]
Math Ann, 2018 Henriot K, Hughes K.
europepmc +1 more source
On Waring's Problem for Cubes and Smooth Weyl Sums
, 2001 J. Brüdern, T. Wooley
semanticscholar +1 more source