Browsing by Subject "Iwasawa theory"

Now showing items 1-5 of 5

  • Computing L-Invariants for the Symmetric Square of an Elliptic Curve

    Delbourgo, Daniel; Gilmore, Hamish Julian (Taylor & Francis, 2019)
    Let E be an elliptic curve over Q, and p≠2 a prime of good ordinary reduction. The p-adic L-function for Sym²E always vanishes at s = 1, even though the complex L-function does not have a zero there. The L-invariant itself ...
  • Heegner cycles and congruences between anticyclotomic p-adic L-functions over CM-extensions

    Delbourgo, Daniel; Lei, Antonio (Electronic Journals Project, 2020)
    Let E be a CM-field, and suppose that f, g are two primitive Hilbert cusp forms over E⁺ of weight 2 satisfying a congruence modulo λʳ. Under appropriate hypotheses, we show that the complex L-values of f and g twisted by ...
  • Higher order congruences amongst hasse-weil L-values

    Delbourgo, Daniel; Peters, Lloyd (Cambridge University Press, 2015-02-03)
    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]. ...
  • Iwasawa theory over solvable three-dimensional p-adic Lie extensions

    Qin, Chao (The University of Waikato, 2018)
    Iwasawa theory is a powerful tool which describes the mysterious relationship between arithmetic objects (motives) and the special values of L-functions. A precise form of this relationship is neatly encoded in the so-called ...
  • K₁-congruences for three-dimensional Lie groups

    Delbourgo, Daniel; Chao, Qin (Springer, 2019)
    We completely describe K₁ (Zₚ [[G∞]]) and its localisations by using an infinite family of p-adic congruences, where G∞ is any solvable p-adic Lie group of dimension 3. This builds on earlier work of Kato when ...