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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $Q$ be a positive-definite quaternary quadratic form with integercoefficients. We study the problem of giving bounds on the largest positiveinteger $n$ that is locally represented by $Q$ but not represented. Assumingthat $n$ is relatively prime to $D(Q)$, the determinant of the Gram matrix of$Q$, we show that $n$ is represented provided that \[  n \gg \max \{ N(Q)^{3/2 + \epsilon} D(Q)^{5/4 + \epsilon}, N(Q)^{2 +\epsilon} D(Q)^{1 + \epsilon} \}. \] Here $N(Q)$ is the level of $Q$. We givethree other bounds that hold under successively weaker local conditions on $n$.  These results are proven by bounding the Petersson norm of the cuspidal partof the theta series, which is accomplished using an explicit formula for theWeil representation due to Scheithauer.

Integers represented by positive-definite quadratic forms and Petersson inner products