Modular Forms: A Problem Book using Pari/GP
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Beschreibung
This is a problem book on modular forms, aimed at graduate students and researchers with an interest in computational aspects of the subject. It assumes some familiarity with classical modular forms, with a brief review provided in the opening chapter. The text is organized into largely independent chapters, each devoted to a specific topic. The first part presents the necessary background and a collection of problems, many involving implementations in Pari/GP; the second part provides solutions and additional material. Full implementations in Pari/GP are available on GitHub.
Topics include differential operators, Eisenstein series, eta quotients, exact computation of L-values at negative integers (notably via half-integral weight methods), orthogonal polynomials and their applications, Fourier expansions at general cusps, nonholomorphic Eisenstein series and related identities, and aspects of complex multiplication, Hauptmoduln, and special values. All implementations are provided as Pari/GP scripts, and the exercise–solution format drives computational engagement.
This is a problem book on modular forms, aimed at graduate students and researchers with an interest in computational aspects of the subject. It assumes some familiarity with classical modular forms, with a brief review provided in the opening chapter. The text is organized into largely independent chapters, each devoted to a specific topic. The first part presents the necessary background and a collection of problems, many involving implementations in Pari/GP; the second part provides solutions and additional material. Full implementations in Pari/GP are available on GitHub.
Topics include differential operators, Eisenstein series, eta quotients, exact computation of L-values at negative integers (notably via half-integral weight methods), orthogonal polynomials and their applications, Fourier expansions at general cusps, nonholomorphic Eisenstein series and related identities, and aspects of complex multiplication, Hauptmoduln, and special values. All implementations are provided as Pari/GP scripts, and the exercise–solution format drives computational engagement.
Presents a unique problem-based approach to advanced topics in modular forms Provides research topics and open questions Includes discussion of computational issues Includes a GitHub repository
Autor*in
Henri Cohen
Themen in »Modular Forms: A Problem Book using Pari/GP«
Modular Forms Pari/GP Eta Quotients Half-Integral Weight Expansions at Cusps Complex Multiplication and Hauptmoduln Apéry-like Recursions Nonholomorphic Eisenstein Series and K-Bessel Functions Special Values