Abstract Let λ 1,…, λ 4 be non-zero real numbers, not all of the same sign, with λ 1/λ 2
irrational, and ϖ be a real number. We prove that for any ε> 0, the inequality| λ 1 p 1+ λ 2 p 2 …

Sum of one prime and two squares of primes in short intervals - ScienceDirect Skip to main
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Abstract Suppose that λ 1, λ 2, λ 3, λ 4 are nonzero real numbers, not all negative, and λ 1/λ
2 is irrational and algebraic. Let V be a well-spaced sequence, δ> 0. It is proved that for any …

We refine a result of the last two Authors of [8] on a Diophantine approximation problem with
two primes and a k-th power of a prime which was only proved to hold for 1< k< 4/3. We …

Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 |
SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a journal …

Abstract Let λ 2, λ 3, λ 4, λ 5 be nonzero real numbers, not all negative. Let V be a well-
spaced sequence. Assume that λ 2/λ 3 is irrational and algebraic, and δ> 0. Let EV, N, δ be …

arXiv:1606.00860v1 [math.NT] 2 Jun 2016 Page 1 arXiv:1606.00860v1 [math.NT] 2 Jun 2016
Riv. Mat. Univ. Parma, Vol. x (2016), 000-000 Alessandro Languasco Applications of some …

Let $ k $ be an integer with $ k\geq 3$ and $\varepsilon\gt 0$. Let $ s (k)=[{(k+ 1)}/{2}] $ and
$\sigma (k)=\min\bigl (2^{s (k)-1},\frac {1}{2} s (k)(s (k)+ 1)\bigr) $. Suppose that $\lambda_1 …

Let k be an integer with k≥ 4 and η be any real number. Suppose that λ 1, λ 2, λ 3, λ 4, λ 5
are nonzero real numbers, not all of the same sign and λ 1/λ 2 is irrational. It is proved that …

We study the distribution of the values of the form $\lambda_1 p_1+\lambda_2
p_2+\lambda_3 p_3^ k $, where $\lambda_1 $, $\lambda_2 $ and $\lambda_3 $ are non …