HIGHER ORDER CONGRUENCES AMONGST HASSE–WEIL -VALUES
HIGHER ORDER CONGRUENCES AMONGST HASSE–WEIL -VALUES
Abstract For the $(d+1)$ -dimensional Lie group $G=\mathbb{Z}_{p}^{\times }\ltimes \mathbb{Z}_{p}^{\oplus d}$ , we determine through the use of $p$ -power congruences a necessary and sufficient set of conditions whereby a collection of abelian $L$ -functions arises from an element in $K_{1}(\mathbb{Z}_{p}\unicode[STIX]{x27E6}G\unicode[STIX]{x27E7})$ . If $E$ is a semistable elliptic curve over …