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      Higher order congruences amongst hasse-weil L-values

      Delbourgo, Daniel; Peters, Lloyd
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      J-Aust-Mathematical-Soc.pdf
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      DOI
       10.1017/S1446788714000445
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      Delbourgo, 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/S1446788714000445
      Permanent Research Commons link: https://hdl.handle.net/10289/9305
      Abstract
      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 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.
      Date
      2015-02-03
      Type
      Journal Article
      Publisher
      Cambridge University Press
      Rights
      This article is published in the Journal of the Australian Mathematical Society. © 2014 Australian Mathematical Publishing Association Inc.
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      • Computing and Mathematical Sciences Papers [1455]
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