Elchin Hasanalizade

activity

20212025

collaborators

7 papers

math.NT2025

Explicit Burgess inequalities for cubefree moduli

Elchin Hasanalizade, Hua Lin, Greg Martin +2

Burgess proved that for $χ_{q}$ a primitive Dirichlet character modulo $q$ with $q$ cubefree, $\sum_{M < n \leq M + N} χ_{q} (n) = O (N^{1 - \frac{1}{r}} q^{\frac{r + 1}{4 r ^{2}} + ε})$ for al…

math.NT2022

Sums of Fibonacci numbers close to a power of 2

Elchin Hasanalizade

In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools…

math.NT2022

On a conjecture of Deaconescu

Elchin Hasanalizade

In 2000 Deaconescu raised a question whether there exists a composite $n$ for which $S_{2} (n) ∣ ϕ (n) - 1$ , where $ϕ (n)$ is Euler's function and $S_{2} (n)$ is Schemmel's totient function. I…

math.NT2022

Remark on a paper by Wu

Elchin Hasanalizade

In this short note, we give an affirmative answer to Wu's conjecture on practical numbers, which was posed in [X.-H. Wu, {\it Special forms and the distribution of practical number…

math.NT2022

On near-perfect numbers of special forms

Elchin Hasanalizade

In this paper we discuss near-perfect numbers of various forms. In particular, we study the existence of near-perfect numbers in the Fibonacci and Lucas sequences, near-perfect val…

math.NT2021

Counting zeros of the Riemann zeta function

Elchin Hasanalizade, Quanli Shen, Peng-Jie Wong

In this article, we show that $N (T) - \frac{T}{2 π} lo g (\frac{T}{2 π e}) \leq 0.1038 lo g T + 0.2573 lo g lo g T + 9.3675$ where $N (T)$ denotes the n…

math.NT2021

Counting zeros of Dedekind zeta functions

Elchin Hasanalizade, Quanli Shen, Peng-Jie Wong

Given a number field $K$ of degree $n_{K}$ and with absolute discriminant $d_{K}$ , we obtain an explicit bound for the number $N_{K} (T)$ of non-trivial zeros (counted with multiplicity),…