Chudnovsky-Ramanujan Type Formulae

In a well-known 1914 paper, Ramanujan gave a number of rapidly converging series for 1/pi which are derived using modular functions of higher level. The Chudnovskys derived an analogous series representation 1/pi, often used in practice for record breaking computations of pi. These formulae have recently been explained in the context of elliptic curves, modular curves, and the Picard-Fuchs differential equation. In particular, these series representations for 1/pi arise from relations between periods of families of elliptic curves and hypergeometric solutions to their associated Picard-Fuch differential equations; we refer to such relations as Chudnovsky-Ramanujan type formulae. The aim of this project is to apply this framework to derive a complete list of Chudnovsky-Ramanujan type formulae. This will be done by identifying the families of elliptic curves suitable for the method and then applying the method on each such family to produce the resulting list of Chudnovsky-Ramanujan type formulae.

Faculty Supervisor:

Imin Chen

Student:

Partner:

Indian Institute of Technology Bombay

Discipline:

Mathematics

Sector:

Education

University:

Simon Fraser University

Program: