Browsing by Subject "Iwasawa theory"
Now showing items 15 of 5

Computing LInvariants 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 padic Lfunction for Sym²E always vanishes at s = 1, even though the complex Lfunction does not have a zero there. The Linvariant itself ... 
Heegner cycles and congruences between anticyclotomic padic Lfunctions over CMextensions
(Electronic Journals Project, 2020)Let E be a CMfield, 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 Lvalues of f and g twisted by ... 
Higher order congruences amongst hasseweil Lvalues
(Cambridge University Press, 20150203)For the (d+1)dimensional Lie group G=Z×pZp⊕d we determine through the use of ppower congruences a necessary and sufficient set of conditions whereby a collection of abelian Lfunctions arises from an element in K₁Zp[G]. ... 
Iwasawa theory over solvable threedimensional padic 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 Lfunctions. A precise form of this relationship is neatly encoded in the socalled ... 
K₁congruences for threedimensional Lie groups
(Springer, 2019)We completely describe K₁ (Zₚ [[G∞]]) and its localisations by using an infinite family of padic congruences, where G∞ is any solvable padic Lie group of dimension 3. This builds on earlier work of Kato when ...