4 papers · 1 filter
Any six points on the Riemann sphere can be split into three pairs by a triple of disjoint discs
Matvey Smirnov
We prove that for any six points on the Riemann sphere there exist three disjoint closed (or open) discs, each of which contains exactly two of the six distinguished points. This s…
Computation of genus 2 Kleinian hyperelliptic functions via Richelot isogenies
Matvey Smirnov
In this work we propose an algorithm that numerically evaluates Kleinian hyperelliptic functions associated with a complex curve of genus 2. This algorithm is based upon constructi…
Kleinian hyperelliptic funtions of weight 2 associated with curves of genus 2
Matvey Smirnov
We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic -function. These functions are related to weight 2…
A Landen-type method for computation of Weierstrass functions
Matvey Smirnov, Kirill Malkov, Sergey Rogovoy
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effec…