Analogs of Dirichlet L-functions in chromatic homotopy theory

“Chromatic ” homotopy theory

Homotopy theory deals with spaces of large but finite dimension. Chromatic homotopy theory is an organizing principle which is highly developed in the stable situation. 1. The Spanier-Whitehead category. We'll work with the category of finite polyhedra (or finite CW complexes) and homotopy classes of continuous maps between them. We will always fix a basepoint in all spaces, and assume that map...

Calculation of Dirichlet L-Functions

A method for calculating Dirichlet L-series is presented along with the theory of residue class characters and their automatic generation. Tables are given of zeros of Lseries for moduli S 24.

On the Order of Dirichlet L-functions

Real zeros of quadratic Dirichlet L - functions

A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...

The Mean-square of Dirichlet L-functions

where α and β are small complex numbers satisfying α, β ≪ 1/ log q. Ingham [Ing] considered an analogous moment for the Riemann zeta-function on the critical line with small shifts. Paley [Pal] considered the moment above for Dirichlet L-functions. Heath-Brown [HB] has computed a similar moment, but for all characters modulo q, in the case that α = β = 0. His result is Theorem 1 (HB). There are...