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El. knyga: Introduction to Applications of Modular Forms: Computational Aspects

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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.  


Recenzijos

This book provides a collection of explicit methods for working with modular forms and applications to number-theoretic problems. It is meant as a complement to the existing literature on modular forms. ... The book contains many snippets of SageMath code, ranging from one line to roughly one page, that illustrate how the results can be applied in practice. (Peter Bruin, Mathematical Reviews, June, 2025)

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

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.
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