Hida families and rational points on elliptic curves Page 1 DOI: 10.1007/s00222-007-0035-4
Invent. math. 168, 371–431 (2007) Hida families and rational points on elliptic curves Massimo …

Let E be a modular elliptic curve over a totally real number field F. We prove the weak
exceptional zero conjecture which links a (higher) derivative of the p-adic L-function …

Using the theory of $(\phi,\Gamma) $-modules we generalize Greenberg's construction of
the $\cal {L} $-invariant to $ p $-adic representations which are semistable at $ p $.\This …

Cet article s' inscrit dans le cadre de la correspondance de Langlands locale p-adique pour
la série principale unitaire de GL2 (Qp). Nous utilisons la théorie des (ϕ, Γ)-modules de …

The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the
group GL2 (K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to …

In earlier work, the first named author generalized the construction of Darmon-style-
invariants for representations of definite unitary groups of arbitrary rank. Finally, we study the …

Let f be a modular eigenform of even weight k≥ 2 and new at a prime p dividing exactly the
level with respect to an indefinite quaternion algebra. The theory of Fontaine–Mazur allows …

p-adic L-functions and the Rationality of Darmon Cycles Page 1 Canad. J. Math. Vol. 64 (5),
2012 pp. 1122–1181 http://dx.doi.org/10.4153/CJM-2011-076-8 c Canadian Mathematical …

Let f∈ S k 0+ 2⁢(Γ 0⁢(N⁢ p)) be a normalized N-new eigenform with p∤ N and such that ap
2≠ pk 0+ 1 and ord p⁡(ap)< k 0+ 1. By Coleman's theory, there is ap-adic family 𝐅 of …

The main purpose of this note is to provide an algorithm for approximating the value of the
balanced p-adic L-function, as constructed in [Hsi21], at the point (2, 1, 1), which is lying …