On the characteristic $p$ valued measure associated to Drinfeld discriminant

Details On the characteristic $p$ valued measure associated to Drinfeld discriminant On the characteristic $p$ valued measure associated to Drinfeld discriminant

2011-09-14

arxiv.org/abs/1109.3006v1

Mathematics

Number Theory

41 pages

Scientific paper

In this paper, after reviewing known results on functions over Bruhat-Tits trees and the theory of characteristic $p$ valued modular forms, we present some structure of the tempered distributions on the projective space ${\P1}(\bk_\infty)$ over a complete function field $\bk_\infty$ of characteristic $p$, and calculate the characteristic $p$ valued measure associated to the Drinfeld discriminant and the characteristic $p$ valued measure associated to the Poinca\'e series.

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