F. Rakhmonov

activity

20242026

collaborators

4 papers

math.NT2026

Generalized Estermann problem for non-integer powers with almost proportional summands

Firuz Rakhmonov, Parviz Rakhmonov

For $H \geq N^{1 - \frac{1}{2 c}} ln^{2} N$ , where $c$ is a fixed non-integer number satisfying $$ \|c\| \ge 3c\left(2^{[c]+1}-1\right)\frac{\ln \ln N}{\ln N}, \qquad c > \frac{4}{3}\le…

math.NT2025

Sum of short exponential sums with prime numbers

Firuz Rakhmonov

For sufficiently large integers $K$ , $x$ , $y$ , and $q$ satisfying $K \leq y < x$ , where $f (u) = I^\pm u^{n} + I^\pm_{n - 1} u^{n - 1} + \dots + I^\pm_{1} u$ is a polynomial of degree $n$ with real co…

math.NT2025

On the ternary Estermann problem with almost proportional summands

Firuz Rakhmonov

For $n \geq 3$ , an asymptotic formula is derived for the number of representations of a sufficiently large natural number $N$ in the form $p_{1} + p_{2} + m^{n} = N$ , where $p_{1}$ , $p_{2}$ $-$ pr…

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…