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math.NT2026
On Sárközy's Local Extrema Conjectures
Alexander P. Mangerel
Let be a multiplicative function, and let . We consider the frequency with which patterns of the form $$ f(n) > ω\max\{f(n-1),f(n+1)\},…
math.NT2026
On a conjecture of Goldmakher
Alexander P. Mangerel
We construct a -bounded completely multiplicative function whose logarithmically-averaged partial sums satisfy $$ \limsup_{x \rightarrow \infty} \frac{\left|\sum_{n \leq x}…
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…