Sunto: Questo articolo considera una successione di equazioni diieren-ziali a derivate parziali non lineari in forma di divergenza del tipo ?div (Q " G(x; N " ru)) = f " ; in un dominio limitato dello spazio n-dimensionale; Q " = Q " (x) e N " = N " (x) sono matrici con coeecenti limitati, N " e' invertibile e la sua matrice inversa R " ha anche coeecenti limitati. La non linearita' e' dovuta a...

It is known that if $p>37$ a prime number and $E/\mathbb{Q}$ an elliptic curve without complex multiplication, then the image of mod $p$ Galois representation $$ \bar{\rho}_{E,p}:\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\rightarrow \operatorname{GL}(E[p]) $E$ either whole $\operatorname{GL}(E[p])$, or \emph{contained} in normaliser non-split Cartan subgroup $\operatorname{GL}(E[p])$....

Let E/Q be an elliptic curve and let p be an odd supersingular prime for E. In this article, we study the simplest case of Iwasawa theory for elliptic curves, namely when E(Q) is finite, X(E/Q) has no p-torsion and the Tamagawa factors for E are all prime to p. Under these hypotheses, we prove that E(Qn) is finite and make precise statements about the size and structure of the p-power part of X...

E(K) ∼= Etor(K)× ZK where Etor(K) is the torsion subgroup of E(K) and r = rK is the rank of E(K). There are many interesting questions about the rank of an elliptic curve that are still open, but the focus of this paper is on the torsion part of E(K). Let p be a prime number, and let E[p] be the Fp-vector space of p-torsion points on E(K), where K is a fixed algebraic closure of K. The natural ...

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Let E be an elliptic curve over Q. We assume that E has good supersingular reduction at a prime p, and for simplicity, assume p is odd and ap = p+ 1− #E(Fp) is zero. Then, as the second author showed, the p-adic L-function Lp,α(E) of E corresponding to α = ±√−p (by Amice-Vélu and Vishik) can be written as Lp,α(E) = f log+p +g logp α by using two Iwasawa functions f and g ∈ Zp[[Gal(Q∞/Q)]] ([20]...

Let p. be a symmetric p-stable measure, 0 < p < 1, on a locally convex separable linear metric space E and let q be a lower semicontinuous seminorm on E. It is known that F(t) = u{x : q(x) < t) is absolutely continuous with respect to the Lebesgue measure. We prove an explicit formula for the density F'(t) and give an asymptotic estimate of it at infinity. 1. Let X be a symmetric Gaussian rando...