Arithmetic properties of modular functions

Robins, Sharon (2018) Arithmetic properties of modular functions. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Sharon Robins (13MS075)) 13MS075.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

The main idea of this thesis to present the proof of the theorem j(Ok) is an algebraic integer. In the first chapter, we discuss elliptic functions and introduce a key example called Weierstrass ℘-function. In the second chapter, we will define what is j-invariant and study its properties. In the last chapter, we will go through the general definition of modular function and see it’s arithmetic properties. Finally, we introduce modular equation and in fact, we will see it is the polynomial required to prove j(Ok) is an algebraic integer.

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