Karimjon Ibrohimjonovich Mirzoabdughafurov

collaborators

3 papers

math.NT2026

Mean Estimates for Short Polynomial Exponential Sums over Primes

Karimjon Ibrohimjonovich Mirzoabdughafurov

Let $n \geq 2$ be a fixed integer, and let $K, x, y$ be positive integers satisfying $2 \leq K \leq y < x$ . Consider a polynomial \[ f(u)=αu^n+α_{n-1}u^{n-1}+\cdots+α_1u+α_0 \] with real coef…

math.NT2026

Intermediate-Range Estimates for Short Weyl Sums and Waring's Problem with Almost Proportional Summands

Karimjon Ibrohimjonovich Mirzoabdughafurov

We obtain a uniform pointwise estimate for short Weyl sums of degree $n \geq 3$ in the intermediate rational-approximation range $$ \frac{1}{qx^{n-2}y}\ll|λ| \ll\frac{1}{qy^{n-1}}. $…

math.NT2026

Short Quartic Exponential Sums in an Intermediate Range and Waring's Problem for Fourth Powers with Almost Equal Summands

Karimjon Ibrohimjonovich Mirzoabdughafurov

This paper is devoted to short quartic Weyl sums in an intermediate range of rational approximations and to their application to Waring's problem with almost equal summands. We obt…