Weight $$\mathbf {1/2}$$ multiplier systems for the group $$\mathbf {\Gamma _0^+({\varvec{p}})}$$ and a geometric formulation

Archiv der Mathematik, vol. 122, pp. 143–153

Abstract

Abstract We construct a weight 1/2 multiplier system for the group $$\Gamma _0^+(p)$$ Γ 0 + ( p ) , the normalizer of the congruence subgroup $$\Gamma _0(p)$$ Γ 0 ( p ) where p is an odd prime, and we define an analogue of the eta function and Rademacher symbol and relate it to the geometry of edge paths in a triangulation of the upper half-plane.

Authors 2

1. Michael H. Mertens corresponding Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Pontdriesch 14/16, 52062, Aachen, Germany

2. Mark Norfleet

   University of Wisconsin–Green Bay

   Affiliation as printed

   University of Wisconsin, Green Bay, Wisconsin, USA