Málstofa: Breki Pálsson

Fyrirlesari: Breki Pálsson (Sorbonne U., Paris)
Titil: Investigating Residue Degrees in Number Fields related to Modular Forms and their Connections to Permutation Cycles.
27. október 2023, kl. 11:40 í stofu V-152 í VR-2, athugið breytta staðsetningu.

Ágrip: Modular forms are a special type of complex analytic functions that have symmetry properties. They are used in various areas of mathematics, such as geometry, number theory, and topology. Hecke operators are C-linear maps that are used to transform these modular forms. When a modular form is an eigenvector for all Hecke operators, it is called a Hecke eigenform. The coefficients of a normalized Hecke eigenform generate a number field called the coefficient field. Number fields allow us to generalize the concept of prime numbers using ideals, and an important characteristic of prime ideals is their residue degrees. This talk aims to explore the relationship between the maximal residue degree of prime ideals in the coefficient field of normalized eigenforms, above a given prime number, and the average maximum length of a cycle in a permutation of ‘n’ elements.