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math.NT2026
Farey Symbols for the Picard Group
Devendra Tiwari, Helena Verrill
We develop Picard Farey symbols for finite-index subgroups of \(G=\PSL_2(\ZZ[i])\) from the Gaussian Farey tessellation of \(\HH^3\) by ideal octahedra. The ambient geometry natura…
math.NT2026
Modular elliptic curves and hyperbolic uniformization
Neil Dummigan, Devendra Tiwari
In an article published a few years before the modularity of elliptic curves over $\Q$ was proved, Mazur \cite{maz} looked at modularity as a purely complex analytic phenomenon, de…
math.NT2026
Shimura curves of discriminant 14 and 15 and associated Heun Functions
Harshavardhan Reddy, Devendra Tiwari
We study the Shimura curves of discriminant for relating specific weight modular forms on these Shimura curves to the associated Heun functions for th…