Abstract Let c 1,…, cs be non-zero integers satisfying c 1+⋯+ cs= 0. We consider the system
c 1 x 1 d+⋯+ csxsd= 0 with d≥ 3, where xi are restricted in subset A of Piatetski-Shapiro …

This paper studies the minimal conditions under which we can establish asymptotic
formulae for Waring's problem and other additive problems that may be tackled by the circle …

Friable values of Piatetski-Shapiro sequences Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 145, Number 10, October 2017, Pages 4255–4268 http://dx.doi.org/10.1090/proc/13621 …

A positive integer n is called square-full if for every prime p| n, also p 2| n. Piatetski–Shapiro
sequences (PS-sequences) are defined by N c=(⌊ nc⌋) n∈ N,(c> 1, c∉ N), where⌊ z⌋ is …

Dans cet article nous donnons une formule asymptotique pour le nombre de représentations
d'un grand entier comme somme de puissances identiques des nombres premiers de …

For all $\alpha_1,\alpha_2\in (1, 2) $ with $1/\alpha_1+ 1/\alpha_2> 5/3$, we show that the
number of pairs $(n_1, n_2) $ of positive integers with $ N=\lfloor {n_1^{\alpha_1}}\rfloor+ …

We consider the nonlinear system $ c_1p_1^ d+ c_2p_2^ d+\dots+ c_s p_s^ d= 0$ with $
c_1, c_2,\dots, c_s\in\mathbb Z $ being nonzero and satisfying $ c_1+ c_2+\dots+ c_s= 0 …

We bound Kloosterman-like sums of the shape\[\sum_ {n= 1}^ N\exp (2\pi i (x\floor {f (n)}+
y\floor {f (n)}^{-1})/p),\] with integers parts of a real-valued, twice-differentiable function $ f $ is …

arXiv:1607.08745v2 [math.NT] 15 May 2017 Page 1 arXiv:1607.08745v2 [math.NT] 15 May
2017 Waring-Goldbach Problem with Piatetski-Shapiro Primes Yıldırım Akbal Ahmet M …

This thesis is a summary of the works of the author. We discuss problems whether a given
set contains arithmetic progressions or not. By Szemerédi's theorem, any subset of positive …