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math.NT2026
On the generation of multiplicative groups by small primes
Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen
Motivated by a question of Regev arising from his improved quantum factoring algorithm, we study how many small primes are needed to generate the group $({\mathbb Z}/q{\mathbb Z})^…
math.NT2026
Small values of signed harmonic sums and logarithmic means of multiplicative functions
Oleksiy Klurman, Marc Munsch, Yu-Chen Sun
We construct sequences with small values of signed harmonic sums \[ \sum_{n\in\mathcal{A}\cap[1,N]}\frac{a_n}{n}, \] for any reas…
math.NT2026
A Halász-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…