Gap orders of meromorphic functions on Riemann surfaces.
Gap orders of rational functions on plane curves with few singular points.
Gap Sequences and Moduli in Genus 4.
Generalised elliptic functions
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstraß ℘-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed...
Generalized SU (2) theta functions.
Generation of class fields by the modular function
Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields
We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.
Genus 3 normal coverings of the Riemann sphere branched over 4 points.
In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.
Groupe des points de Weierstrass sur une famille de quartiques lisses