5 papers
Near-optimal density theorems for large dilates of large point configurations
Vjekoslav Kovač, Adian Anibal Santos Sepčić
We study density thresholds that force a measurable set to contain all sufficiently large similar copies of every -point configuration. We prove a lower…
Sharp variational inequalities for the Hardy-Littlewood maximal operator on finite undirected graphs
Cristian González-Riquelme, Vjekoslav Kovač, José Madrid
We study sharp -variational inequalities for the Hardy-Littlewood maximal operator on complete graphs, answering in the affirmative a question by Feng Liu and Qingying Xue. We a…
On the number of divisors of Mersenne numbers
Vjekoslav Kovač, Florian Luca
Denote , where is the number of divisors function. Motivated by a question of Paul Erdős, we show that the sequence of ratios is…
On the irrationality of certain super-polynomially decaying series
Tonći Crmarić, Vjekoslav Kovač
We give a negative answer to a question by Paul Erdős and Ronald Graham on whether the series \[ \sum_{n=1}^{\infty} \frac{1}{(n+1)(n+2)\cdots(n+f(n))} \] has an irrational sum whe…
Variational estimates for martingale paraproducts
Vjekoslav Kovač, Pavel Zorin-Kranich
We show that bilinear variational estimates of Do, Muscalu, and Thiele (arXiv:1009.5187) remain valid for a pair of general martingales with respect to the same filtration. Our res…