Lecture
Petersson Inner Product and Hecke Operators
In course
DEMO: qui mollit
Et do pariatur non mollit incididunt minim irure dolor. Nostrud non fugiat cupidatat pariatur deserunt occaecat fugiat proident. Ea amet enim pariatur minim quis nulla tempor magna cillum anim ex in do ullamco. Est ex ex tempor laboris aliquip ex dolore laboris aute proident. Laboris ex ex cupidatat fugiat officia ullamco.
Description
This lecture introduces the Petersson inner product, a fundamental concept in the theory of modular forms, and explores the definition and properties of Hecke operators, crucial tools in the study of modular forms as functions on lattices. The lecture also covers the translation of Hecke operators to the language of matrices and their normalization. Additionally, it discusses the equivalence of different definitions of Hecke operators and their implications on Fourier coefficients, providing insights into the structure and completeness of certain collections of matrices.
Instructor
veniam est aute
Eiusmod aute ut nisi minim commodo ea aliquip quis aliquip non consequat minim amet. Qui cupidatat ut excepteur esse adipisicing ullamco deserunt mollit laboris consectetur adipisicing. In pariatur ullamco in esse laboris laboris esse ullamco et aute minim quis amet. Adipisicing deserunt qui voluptate sunt culpa ullamco anim duis sit ullamco. Veniam amet dolore laborum veniam culpa eu Lorem dolor. Officia laboris pariatur nulla commodo in ut do aliqua enim ullamco veniam est consectetur. Cillum culpa reprehenderit proident nulla id voluptate cillum excepteur occaecat duis.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (37)
Monster Group: Representation
Explores the Monster group, a sporadic simple group with a unique representation theory.
Theta functions: Properties and Transformations
Explores the properties and transformations of theta functions, including modular forms and lattice levels.
Meromorphic Functions & Differentials
Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.
Real Functions: Definitions and Examples
Explores definitions and examples of real functions of a real variable.
Relations in Computer Science
Explores the properties of relations in computer science, including equivalence relations and the partition of a set.