Delbourgo, DanielPeters, Lloyd2015-04-292015-02-032015-04-292015-02-03Delbourgo, D., & Peters, L. (2015). Higher order congruences amongst hasse-weil L-values. Journal of the Australian Mathematical Society, 98(1), 1–38. http://doi.org/10.1017/S14467887140004451446-7887https://hdl.handle.net/10289/9305For 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 K₁Zp[G]. If E is a semistable elliptic curve over 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.application/pdfengThis article is published in the Journal of the Australian Mathematical Society. © 2014 Australian Mathematical Publishing Association Inc.elliptic curvesIwasawa theoryK-theoryL-functionsJournal Article10.1017/S14467887140004451446-8107