The functional equation for Dirichlet L-functions

Monday, May 11, 2020 - 4:00pm
Zoom presentation
Spenser Rook
(MU Math)

We first study the properties of special homomorphisms on finite abelian groups which are known as characters. When defined on the multiplicative group of residue classes modulo q, these maps form Dirichlet characters, which are used to define L-functions, an important generalization of the Riemann zeta function. The main result is that L-functions satisfy a functional equation which is closely related to the Gamma function.

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