18 citations · 56 across the 14 of their papers we have counts for
18 papers
Algorithms for hyperelliptic Mumford Curves -adic Uniformization, -adic integrals and -adic heights
Enis Kaya, Marc Masdeu, J. Steffen Müller +1
Mumford curves generalize the Tate uniformization of elliptic curves with split multiplicative reduction and provide p-adic analogues of the uniformization of Riemann surfaces. In…
Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points
Lennart Gehrmann, Xavier Guitart, Marc Masdeu
We develop the tools required to effectively evaluate the Bianchi rigid meromorphic cocycles introduced by Darmon-Gehrmann-Lipnowski at big ATR points, and use them to obtain the f…
Plectic p-adic invariants
Michele Fornea, Xavier Guitart, Marc Masdeu
For modular elliptic curves over number fields of narrow class number one, and with multiplicative reduction at a collection of p-adic primes, we define new p-adic invariants. Insp…
A quaternionic construction of -adic singular moduli
Xavier Guitart, Marc Masdeu, Xavier Xarles
Rigid meromorphic cocycles were introduced by Darmon and Vonk as a conjectural -adic extension of the theory of singular moduli to real quadratic base fields. They are certain c…
Special values of triple-product -adic -functions and non-crystalline diagonal classes
Francesca Gatti, Xavier Guitart, Marc Masdeu +1
The main purpose of this note is to understand the arithmetic encoded in the special value of the -adic -function associat…
An automorphic approach to Darmon points
Xavier Guitart, Marc Masdeu, Santiago Molina
We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-triv…
Periods of modular GL2-type abelian varieties and p-adic integration
Xavier Guitart, Marc Masdeu
Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain addi…
Uniformization of modular elliptic curves via p-adic periods
Xavier Guitart, Marc Masdeu, Mehmet Haluk Sengun
The Langlands Programme predicts that a weight 2 newform f over a number field K with integer Hecke eigenvalues generally should have an associated elliptic curve E_f over K. In ou…
Poincaré duality isomorphisms in tensor categories
Marc Masdeu, Marco A. Seveso
If for a vector space V of dimension g over a characteristic zero field we denote by its alternating powers, and by its linear dual, then there are natural Poi…
Dirac operators in tensor categories and the motive of quaternionic modular forms
Marc Masdeu, Marco Adamo Seveso
We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weight…
Darmon points on elliptic curves over number fields of arbitrary signature
Xavier Guitart, Marc Masdeu, Mehmet Haluk Sengun
We present new constructions of complex and p-adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present…
A -adic construction of ATR points on -curves
Xavier Guitart, Marc Masdeu
In this note we consider certain elliptic curves defined over real quadratic fields isogenous to their Galois conjugate. We give a construction of algebraic points on these curves…
Overconvergent cohomology and quaternionic Darmon points
Xavier Guitart, Marc Masdeu
We develop the (co)homological tools that make effective the construction of the quaternionic Darmon points introduced by Matthew Greenberg. In addition, we use the overconvergent…
Elementary Matrix Decomposition and The Computation of Darmon Points with Higher Conductor
Xavier Guitart, Marc Masdeu
We extend the algorithm of Darmon-Green and Darmon-Pollack for computing p-adic Darmon points on elliptic curves to the case of composite conductor. We also extend the algorithm of…
Computation of ATR Darmon points on non-geometrically modular elliptic curves
Xavier Guitart, Marc Masdeu
ATR points were introduced by Darmon as a conjectural construction of algebraic points on certain elliptic curves for which in general the Heegner point method is not available. So…
Computing fundamental domains for the Bruhat-Tits tree for GL2(Qp), p-adic automorphic forms, and the canonical embedding of Shimura curves
Cameron Franc, Marc Masdeu
We describe an algorithm for computing certain quaternionic quotients of the Bruhat-Tits tree for GL2(Qp). As an application, we describe an algorithm to obtain (conjectural) equat…
CM cycles on Shimura curves, and p-adic L-functions
Marc Masdeu
Let f be a modular form of weight k>=2 and level N, let K be a quadratic imaginary field, and assume that there is a prime p exactly dividing N. Under certain arithmetic conditions…
Continued fractions in 2-stage euclidean quadratic fields
Xavier Guitart, Marc Masdeu
We discuss continued fractions on real quadratic number fields of class number 1. If the field has the property of being 2-stage euclidean, a generalization of the euclidean algori…