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

Studies of modular linear differential equations (MLDE) for theclassification of rational CFT characters have been limited to the case wherethe coefficient functions (in monic form) have no poles, or poles at specialpoints of moduli space. Here we initiate an exploration of the vast territoryof MLDEs with two characters and any number of poles at arbitrary points ofmoduli space. We show how to parametrise the most general equation preciselyand count its parameters. Eliminating logarithmic singularities at all thepoles provides constraint equations for the accessory parameters. By takingsuitable limits, we find recursion relations between solutions for differentnumbers of poles. The cases of one and two movable poles are examined in detailand compared with predictions based on quasi-characters to find completeagreement. We also comment on the limit of coincident poles. Finally we showthat there exist genuine CFT corresponding to many of the newly-studied cases.We emphasise that the modular data is an output, rather than an input, of ourapproach.

Modular Differential Equations with Movable Poles and Admissible RCFT Characters