46 citations · 413 across the 115 of their papers we have counts for
6 papers · 1 filter
The quotient set of the quadratic distance set over finite fields
Alex Iosevich, Doowon Koh, Firdavs Rakhmonov
Let be the -dimensional vector space over the finite field with elements. For each non-zero in and ,…
Sums of Powers in Large Finite Fields: A Mix of Methods
Vitaly Bergelson, Andrew Best, Alex Iosevich
Can any element in a sufficiently large finite field be represented as a sum of two th powers in the field? In this article, we recount some of the history of this problem, touc…
A variant of Waring's Problem for the ring of integers modulo n
David Covert, Alex Iosevich, Jonathan Pakianathan
We study a variant of Waring's problem for , the ring of integers modulo : For a fixed integer , what is the minimum number of th powers necessary…
The square root law and structure of finite rings
A. Iosevich, B. Murphy, J. Pakianathan
Let be a finite ring and define the hyperbola . Suppose that for a sequence of finite odd order rings of size tending to infinity, the follow…
Sums and products in finite fields: an integral geometric viewpoint
Derrick Hart, Alex Iosevich
We prove that if is such that then where $$A^2=\{a \cdot a': a,a'…
Erdos-Falconer distance problem, exponential sums, and Fourier analytic approach to incidence theorems in vector spaces over finite fields
Alex Iosevich, Doowon Koh
We prove several incidence theorems in vector spaces over finite fields using bounds for various classes of exponential sums and apply these to Erdos-Falconer type distance problem…