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Lectures on Modular Forms—
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The Story
This concise volume presents an expository account of the theory of modular forms and its application to number theory and analysis. Suitable for advanced undergraduates and graduate students in mathematics, the treatment starts with classical material and leads gradually to modern developments. Prerequisites include a grasp of the elements of complex variable theory, group theory, and number theory.
The opening chapters define modular forms, develop their most important properties, and introduce the Hecke modular forms. Subsequent chapters explore the automorphisms of a compact Riemann surface, develop congruences and other arithmetic properties for the Fourier coefficients of Klein's absolute modular invariant, and discuss analogies with the Hecke theory as well as with the Ramanujan congruences for the partition function. Substantial notes at the end of each chapter provide detailed explanations of the text's more difficult points.
The opening chapters define modular forms, develop their most important properties, and introduce the Hecke modular forms. Subsequent chapters explore the automorphisms of a compact Riemann surface, develop congruences and other arithmetic properties for the Fourier coefficients of Klein's absolute modular invariant, and discuss analogies with the Hecke theory as well as with the Ramanujan congruences for the partition function. Substantial notes at the end of each chapter provide detailed explanations of the text's more difficult points.
Reprint of the National Bureau of Standards, Washington, DC, 1969 edition.
non-fiction; mathematical studies; mathematics; theory of modular forms; modular forms; group theory; number theory; complex analysis mathematics; hecke modular forms; variable theory; automorphisms of a compact riemann surface; fourier coefficients of klein's absolute modular invariant; phenomenon; theoretical; complex,Description
This concise volume presents an expository account of the theory of modular forms and its application to number theory and analysis. Suitable for advanced undergraduates and graduate students in mathematics, the treatment starts with classical material and leads gradually to modern developments. Prerequisites include a grasp of the elements of complex variable theory, group theory, and number theory.
The opening chapters define modular forms, develop their most important properties, and introduce the Hecke modular forms. Subsequent chapters explore the automorphisms of a compact Riemann surface, develop congruences and other arithmetic properties for the Fourier coefficients of Klein's absolute modular invariant, and discuss analogies with the Hecke theory as well as with the Ramanujan congruences for the partition function. Substantial notes at the end of each chapter provide detailed explanations of the text's more difficult points.
The opening chapters define modular forms, develop their most important properties, and introduce the Hecke modular forms. Subsequent chapters explore the automorphisms of a compact Riemann surface, develop congruences and other arithmetic properties for the Fourier coefficients of Klein's absolute modular invariant, and discuss analogies with the Hecke theory as well as with the Ramanujan congruences for the partition function. Substantial notes at the end of each chapter provide detailed explanations of the text's more difficult points.
Reprint of the National Bureau of Standards, Washington, DC, 1969 edition.
non-fiction; mathematical studies; mathematics; theory of modular forms; modular forms; group theory; number theory; complex analysis mathematics; hecke modular forms; variable theory; automorphisms of a compact riemann surface; fourier coefficients of klein's absolute modular invariant; phenomenon; theoretical; complex,
