Introduction to Applications of Modular Forms

Computational Aspects

Zafer Selcuk Aygin (Autor)

Buch | Hardcover

X, 169 Seiten

2023 | 2023
Springer International Publishing (Verlag)
978-3-031-32628-8 (ISBN)

Artikel merken

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.

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.

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

Erscheinungsdatum	15.07.2023
Reihe/Serie	Synthesis Lectures on Mathematics & Statistics
Zusatzinfo	X, 169 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Gewicht	472 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Dedekind eta Function • Eisenstein series • Modular Forms • Partitions • q-series • quadratic forms • Siegel's Formula • Siegel’s Formula
ISBN-10	3-031-32628-8 / 3031326288
ISBN-13	978-3-031-32628-8 / 9783031326288
Zustand	Neuware