Introduction to Applications of Modular Forms: Computational Aspects

ISBN-13: 9783031326288 / Twarda / 2023 / 169 str.

Zafer Selcuk Aygin

Spis treści

Dirichlet Characters.- Modular Forms: Definition and Some Properties.- Application: Quadratic Forms.- Application: Eta Quotients.- Various Applications.

O autorze

Zafer Selcuk Aygin obtained his PhD from Carleton University in 2016. Since then, he has held two prestigious postdoctoral fellowships, one at Nanyang Technological University in Singapore and the other at the University of Calgary (supported by Pacific Institute for the Mathematical Sciences). He is currently an Instructor at Northwestern Polytechnic and an Adjunct Professor at Carleton University. His main research interest is arithmetic aspects of modular forms.

Blurb

This book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures.

In addition, this book:

• Describes the theory of modular forms and its applications in number theoretic problems
• Provides a resource for people who study or work on the computational aspects of classical modular forms
• Includes computer algorithms to help readers conjecture new results and prove them using the presented theory