Rishi Kumar

collaborators

3 papers

math.NT2024

Exceptional Points for Density Modulo 1

Daniel Berend, Michael D. Boshernitzan, Grigori Kolesnik +1

It is well known that almost every dilation of a sequence of real numbers, that diverges to $\infty$ , is dense modulo~1. This paper studies the exceptional set of points -- those f…

math.PR2024

Exact expressions for the maximal probability that all $k$ -wise independent bits are 1

Daniel Berend, Philip A. Ernst, Aryeh Kontorovich +1

Let $M (n, k, p)$ denote the maximum probability of the event $X_{1} = X_{2} = \dots = X_{n} = 1$ under a $k$ -wise independent distribution whose marginals are Bernoulli random variables w…

math.NT2024

Simultaneous visibility in the integer lattice

Daniel Berend, Rishi Kumar, Andrew Pollington

Two lattice points are visible from one another if there is no lattice point on the open line segment joining them. Let $S$ be a finite subset of $Z^{k}$ . The asymptotic den…

Exceptional Points for Density Modulo 1

Exact expressions for the maximal probability that all k-wise independent bits are 1

Simultaneous visibility in the integer lattice

Exact expressions for the maximal probability that all $k$ -wise independent bits are 1