Aygin, Zafer Selcuk.
Introduction to Applications of Modular Forms Computational Aspects / [electronic resource] : by Zafer Selcuk Aygin. - 1st ed. 2023. - X, 169 p. 1 illus. online resource. - Synthesis Lectures on Mathematics & Statistics, 1938-1751 . - Synthesis Lectures on Mathematics & Statistics, .
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.
9783031326295
10.1007/978-3-031-32629-5 doi
Mathematics.
Mathematics--Data processing.
Number theory.
Mathematics.
Computational Mathematics and Numerical Analysis.
Computational Number Theory.
QA1-939
510
Introduction to Applications of Modular Forms Computational Aspects / [electronic resource] : by Zafer Selcuk Aygin. - 1st ed. 2023. - X, 169 p. 1 illus. online resource. - Synthesis Lectures on Mathematics & Statistics, 1938-1751 . - Synthesis Lectures on Mathematics & Statistics, .
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.
9783031326295
10.1007/978-3-031-32629-5 doi
Mathematics.
Mathematics--Data processing.
Number theory.
Mathematics.
Computational Mathematics and Numerical Analysis.
Computational Number Theory.
QA1-939
510