Higher order congruences amongst Hasse-Weil L-values

Daniel Delbourgo, Lloyd Peters

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4 Citations (Scopus)


For the (d+1)-dimensional Lie group G=Z× pZp ⊕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 K1ZpG. If E is a semistable elliptic curve over \mathbb{Q}, these abelian L-functions already exist; therefore, one can obtain many new families of higher order p-adic congruences. The first layer congruences are then verified computationally in a variety of cases.
Original languageEnglish
Pages (from-to)1-38
Number of pages38
JournalJournal of the Australian Mathematical Society
Issue number1
Publication statusPublished - 2015


  • elliptic curves
  • Iwasawa theory
  • K-theory
  • L-functions

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