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Mathematics - Number Theory and Discrete Mathematics | Computations with Modular Forms - Proceedings of a Summer School and Conference, Heidelberg, August/September

Computations with Modular Forms

Proceedings of a Summer School and Conference, Heidelberg, August/September 2011

Böckle, Gebhard, Wiese, Gabor (Eds.)

2014, XII, 376 p. 29 illus., 12 illus. in color.

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  • Unites lecture notes and research articles; lecture notes prepare the reader for most research articles
  • Covers latest developments in algorithmic aspects of modular forms
  • Targeted at graduate students and researchers in algorithmic number theory and modular forms

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment.

The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field.

The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols.

The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.

Content Level » Research

Keywords » algorithms - cohomology of arithmetic groups - computations in number theory - computations of cohomology groups - modular and automorphic forms

Related subjects » Algebra - Computational Science & Engineering - Number Theory and Discrete Mathematics

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