35 citations · 115 across the 21 of their papers we have counts for
6 papers · 1 filter
A Structure Sheaf for Kirch Topology
Alexander Borisov
Kirch topology on goes back to 1969, and is remarkable for being Hausdorff, connected, and locally connected. In this sense, it is analogous to the usual topology on $\…
Geometrically Nilpotent Subvarieties
Alexander Borisov
We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteratio…
Some Interesting Integer Polynomial Maps
Alexander Borisov
We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.
Quotient singularities, integer ratios of factorials and the Riemann Hypothesis
Alexander Borisov
The goal of this paper is to reveal a close connection between the following three subjects that have not been studied together in the past: terminal and canonical cyclic quotient…
Quantum integers and cyclotomy
Alexander Borisov, Yang Wang, Melvyn B. Nathanson
A sequence of functions {f_n(q)}_{n=1}^{\infty} satisfies the functional equation for multiplication of quantum integers if f_{mn}(q) = f_m(q)f_n(q^m) for all positive integers m a…
On a Question of Craven and a Theorem of Belyi
Alexandr Borisov
In this elementary note we prove that a polynomial with rational coefficients divides the derivative of some polynomial which splits in $\Q$ if and only if all of its irrational ro…