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On the Computation of p-adic Theta Functions arising from the Hurwitz Quaternions

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On the Computation of p-adic Theta Functions arising from the Hurwitz Quaternions

Negrini, Isabella (2017) On the Computation of p-adic Theta Functions arising from the Hurwitz Quaternions. Masters thesis, Concordia University.

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Abstract

The aim of this thesis is to give an efficient method to compute a certain theta function Θ(a,b;z), up to a given p-adic precision n. The function Θ(a,b;z) arises from the Hurwitz quaternions and is meromorphic on the upper-half plane. We will first discuss a ”na¨ıve” method to compute Θ(a,b;z) and, by counting Hurwitz quaternions of a given norm, we will show that this method is not efficient. We will then develop some recursive relations for the Hurwitz quaterions, which will be the fundamental tool to describe a more efficient way to compute Θ(a,b;z).

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Negrini, Isabella
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:23 July 2017
Thesis Supervisor(s):Iovita, Adrian
ID Code:982803
Deposited By: Isabella Negrini
Deposited On:16 Nov 2017 17:36
Last Modified:18 Jan 2018 17:55
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