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 arXiv:1603.03910 [math.NT] we introduced some $C_{n}$ in $Z/2[t]$ definedby a linear recurrence and showed that each $C_{n}$, $n\equiv 0 \bmod{4}$, is asum of $C_{k}$, $k<n$. Combining this with results from arXiv:1508.07523[math.NT] we proved that the space $K$, consisting of those odd mod~2 modularforms of level $\Gamma_{0}(3)$ that are annihilated by the operator $U_{3}+I$,has a basis $m_{i,j}$ "adapted to $T_{7}$ and $T_{13}$" in the sense of Nicolasand Serre. (And so the "completed shallow Hecke algebra" attached to $K$ is apower series ring in $T_{7}$ and $T_{13}$.)  This note derives analogous results in level $\Gamma_{0}(5)$. Now $U_{3}+I$is replaced by $U_{5}+I$, and the operators $T_{7}$ and $T_{13}$ by $T_{3}$ and$T_{7}$. In place of level $\Gamma_{0}(3)$ results from 1508.07523, we uselevel $\Gamma_{0}(5)$ results from arXiv:1603.07085 [math.NT]. A linearrecurrence again plays the key role. Now $C_{n+6} = C_{n+5} +(t^{6}+t^{5}+t^{2}+t)C_{n}+t^{n}(t^{2}+t)$, $C_{0}=0$, $C_{1}=C_{2}=1$,$C_{3}=t$, $C_{4}=t^{2}$, $C_{5}=t^{4}+t^{2}+t$, and we prove that each$C_{n}$, $n\equiv 0$ or $2\bmod{6}$ is a sum of $C_{k}$, $k<n$.

A characteristic 2 recurrence related to $U_{5}$, with a Hecke algebra application