Particle Knots in Toric Modular Space

Linking Numbers of Modular Knots

§1. In this note we examine some questions about closed geodesics on the modular surface X which are suggested by the spectacular pictures from Ghys’ talk [G] as well as his paper with Leys [G-L]. The discussion below follows closely my letter to Mozzochi [Sa1] and as is done there we will only outline the proofs of the main results. Detailed proofs of the delicate estimates that are needed wil...

Double Sequence Iterations for Strongly Contractive Mapping in Modular Space

In this paper, we consider double sequence iteration processes for strongly $rho$-contractive mapping in modular space. It is proved, these sequences, convergence strongly to a fixed point of the strongly $rho$-contractive mapping.

A not on modular hyperconvex space

A note on modular hyperconvex space

On Toric Varieties and Modular Forms

Let M∗(l) = M∗(Γ1(l),C) be the ring of holomorphic modular forms on Γ1(l). In this talk we use the combinatorics of complete toric varieties to construct a subring T∗(l) ⊂ M∗(l), the subring of toric modular forms (§2). This is a natural subring, in the sense that it behaves nicely with respect to natural operations on M∗(l) (namely, Hecke operators, Fricke involution, and the theory of oldform...