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

In their 2015 paper, Mertens and Rolen prove that for a certain level 6"almost holomorphic" modular function $P$, the degree of $P(\tau)$ over$\mathbb{Q}$ for quadratic $\tau$ is as large as expected, settling aconjecture of Bruinier and Ono. Analogously for level 1 modular functions $f$,we expect $\mathbb{Q}(f(\tau))$ to have similar degree to$\mathbb{Q}(j(\tau))$. In this paper, I show for a wide class of level 1 almostholomorphic modular functions that\[\dfrac{1}{M}[\mathbb{Q}(j(\tau)):\mathbb{Q}]\leq[\mathbb{Q}(f(\tau)):\mathbb{Q}]\leq[\mathbb{Q}(j(\tau)):\mathbb{Q}]\] for allquadratic $\tau$ and some constant $M$. This is proven using techniques ofo-minimality, and hence can easily be made uniform; the constant $M$ dependsonly upon the "degree" of $f$ (in a certain well-defined sense).

A Note on the Degree of Field Extensions Involving Classical and Nonholomorphic Singular Moduli