Making imprimitive Dirichlet characters behave primitively
Document Type
Lecture
Publication Date
4-24-2014
Abstract
Given a Dirichlet character Χ mod q, it is traditional to extend Χ to all of Z/qZ by declaring that Χ(n) = 0 when (n,q) ≠ 1. When Χ is primitive (i.e. not induced by a Dirichlet character mod d for some proper divisor d of q), this extension endows the associated Gauss sum and L-function with properties that are lost when Χ is imprimitve. In this talk we will introduce a modification to the traditional extension of imprimitive characters which causes them to behave primitively, in the sense that the relevant properties of the Gauss sum and L-function take on the form usually only associated to primitive characters.
Relational Format
presentation
Recommended Citation
Daleida, Ryan, "Making imprimitive Dirichlet characters behave primitively" (2014). Algebra/Number Theory Seminar. 39.
https://egrove.olemiss.edu/math_algebra_number_theory/39
