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Introduction to Applications of Modular Forms [electronic resource] : Computational Aspects / by Zafer Selcuk Aygin.

By: Aygin, Zafer Selcuk [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mathematics & Statistics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2023Edition: 1st ed. 2023.Description: X, 169 p. 1 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031326295.Subject(s): Mathematics | Mathematics -- Data processing | Number theory | Mathematics | Computational Mathematics and Numerical Analysis | Computational Number TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 510 Online resources: Click here to access online
Contents:
Dirichlet Characters -- Modular Forms: Definition and Some Properties -- Application: Quadratic Forms -- Application: Eta Quotients -- Various Applications.
In: Springer Nature eBookSummary: 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.
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Dirichlet Characters -- Modular Forms: Definition and Some Properties -- Application: Quadratic Forms -- Application: Eta Quotients -- Various Applications.

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.

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