Browsing by Subject "Iwasawa theory"
Now showing items 1-5 of 5
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Computing L-Invariants for the Symmetric Square of an Elliptic Curve
(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
(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
(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
(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
(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 ...
