English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $\Gamma_{F,n}$ be the Hermitian modular group of degree $n>1$ in sense ofHel Braun with respect to an imaginary quadratic field $F$. Let $r$ be anatural number. There exists a multiplier system of weight $1/r$ (equivalentlya Hermitian modular form of weight $k+1/r$, $k$ integral) on some congruencegroup if and only if $r=1$ or $2$. This follows from a much more generalconstruction of Deligne [De] combining it with results of Hill [Hi], Prasad [P]and Prasad-Rapinchuk [PR]. As far as we know, the systems of weight $1/2$ havenot yet been described explicitly. Remarkably Haowu Wang [Wa] gave an exampleof a modular form of half integral weight. Actually he constructs a Borcherdsproduct of weight $23/2$ for a group of type $O(2,4)$. This group is isogenousto the group $U(2,2)$ that contains the Hermitian modular groups of degree two.In this paper we want to study such multiplier systems. If one restricts themto the unimodular group one obtains a usual character. Our main result statesthat the kernel of this character is a non-congruence subgroup. Forsufficiently small $\Gamma$ it coincides with the group described by Kubota inthe case $n=2$ and by Bass Milnor Serre in the case $n>2$.

Multiplier systems for Hermitian modular groups