Results 11 to 20 of about 188 (37)
Effective identifiability criteria for tensors and polynomials [PDF]
, 2017 A tensor $T$, in a given tensor space, is said to be $h$-identifiable if it admits a unique decomposition as a sum of $h$ rank one tensors. A criterion for $h$-identifiability is called effective if it is satisfied in a dense, open subset of the set of ...
Massarenti, Alex +2 more
core +2 more sources
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
Relations between exceptional sets for additive problems [PDF]
, 2010 We describe a method for bounding the set of exceptional integers not represented by a given additive form in terms of the exceptional set corresponding to a subform. Illustrating our ideas with examples stemming from Waring's problem for cubes, we show,
Kawada, Koichi, Wooley, Trevor D.
core +3 more sources
Sums of two squares and a power
, 2016 We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a
C. Hooley +10 more
core +1 more source
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.
core +2 more sources
On the Waring–Goldbach problem for seventh and higher powers [PDF]
, 2016 We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function $H(k)$ in the Waring-Goldbach problem. We obtain new results for all exponents $k \ge 7$, and in particular establish that for large $k$ one has \[H(k)\le (4k ...
Kumchev, Angel, Wooley, Trevor D
core +3 more sources
On Waring's problem: two squares and three biquadrates [PDF]
, 2013 We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing
Friedlander, John B., Wooley, Trevor D.
core +2 more sources
, 2015 Estimates are provided for $s$th moments of cubic smooth Weyl sums, when $4\le s\le 8$, by enhancing the author's iterative method that delivers estimates beyond classical convexity.
Wooley, Trevor D.
core +1 more source
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.
core
On the Waring problem for polynomial rings
, 2011 In this note we discuss an analog of the classical Waring problem for C[x_0, x_1,...,x_n]. Namely, we show that a general homogeneous polynomial p \in C[x_0,x_1,...,x_n] of degree divisible by k\ge 2 can be represented as a sum of at most k^n k-th powers
Fröberg, Ralf +2 more
core +2 more sources