Alexander P. Mangerel

activity

20242026

collaborators

6 papers

math.NT2026

On a conjecture of Goldmakher

Alexander P. Mangerel

We construct a $1$ -bounded completely multiplicative function $f$ whose logarithmically-averaged partial sums satisfy $$ \limsup_{x \rightarrow \infty} \frac{\left|\sum_{n \leq x}…

math.NT2026

A HalÃ¡sz-type asymptotic formula for logarithmic means and its consequences

Oleksiy Klurman, Alexander P. Mangerel

We establish an asymptotic formula for the logarithmic mean value of a 1-bounded multiplicative function that is sharp in many cases of interest. We derive from it a variety of app…

math.NT2025

Sharp bounds for maximal sums of odd order Dirichlet characters

Alexander P. Mangerel

Let $g \geq 3$ be fixed and odd, and for large $q$ let $I ¨ $ be a primitive Dirichlet character modulo $q$ of order $g$ . Conditionally on GRH we improve the existing upper bounds in…

math.NT2025

On a rigidity property for quadratic Gauss sums

Alexander P. Mangerel

Let $N$ be a large prime and let $c > 1/4$ . We prove that if $f$ is a $\pm 1$ -valued completely multiplicative function, such that the exponential sums $$ S_f(a) := \sum_{1 \leq n…

math.NT2024

On Shusterman's Goldbach-type problem for sign patterns of the Liouville function

Alexander P. Mangerel

Let $I^»$ be the Liouville function. Assuming the Generalised Riemann Hypothesis for Dirichlet $L$ -functions (GRH), we show that for every sufficiently large even integer $N$ there…

math.NT2024

On Equal Consecutive Values of Multiplicative Functions

Alexander P. Mangerel

Let $f : N \to C$ be a multiplicative function for which $p : ∣ f (p) ∣ \neq = 1 \sum \frac{1}{p} = \infty.$ We show under this condition alone that for any in…