Z. Rakhmonov

collaborators

4 papers

math.NT2025

Distribution of products of shifted primes in arithmetic progressions with increasing difference

Zarullo Rakhmonov

We obtain an asymptotic formula for the number of primes $p \leq x_{1}$ , $p \leq x_{2}$ such that $p_{1} (p_{2} + a) \equiv l (mod q)$ with $(a, q) = (l, q) = 1$ , $q \leq x^{I^º_{0}}$ , $x_{1} \geq x^{1 - I^\pm}$ ,…

math.NT2025

Sums of values of non-principal characters over shifted primes

Zarullo Rakhmonov

For a nonprincipal character $I ¨ $ modulo $D$ , when $x \geq D^{\frac{5}{6} + ε}$ , $(l, D) = 1$ , we prove a nontrivial estimate of the form $\sum_{n\le x}Î(n)Ï(n-l)\ll x\exp\left(…

math.NT2025

On the mean values of the Chebyshev functions and their applications

Z. Rakhmonov, O. Nozirov

When solving a number of problems in prime number theory, it is sufficient that $t (x; q)$ admits an estimate close to this one. The best known estimates for $t (x; q)$ previously belo…

math.NT2024

Waring's problem with almost proportional summands

Zarullo Rakhmonov, Firuz Rakhmonov

For $n \geq 3$ , an asymptotic formula is derived for the number of representations of a sufficiently large natural number $N$ as a sum of $r = 2^{n} + 1$ summands, each of which is a…