Adel Betina

activity

20152025

most citedArithmetic of p-irregular modular forms: families and p-adic L-functions

6 citations · 11 across the 7 of their papers we have counts for

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math.NT2025

The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators

Adel Betina, Alexandre Maksoud, Alice Pozzi

A complete description of the local geometry of the $p$ -adic eigencurve at $p$ -irregular classical weight one cusp forms is given in the cases where the usual $R = T$ methods fall sh…

math.NT2022★ 1 cited

CM congruence and trivial zeros of the Katz $p$ -adic $L$ -functions for CM fields

Adel Betina, Ming-Lun Hsieh

The aim of this paper is to investigate the trivial zeros of the Katz $p$ -adic $L$ -functions by the CM congruence. We prove the existence of trivial zeros of the Katz $p$ -adic $L$ -…

math.NT2020

A geometric view on Iwasawa theory

Adel Betina, Mladen Dimitrov

This article extends our study of the geometry of the $p$ -adic eigencurve at a point defined by a weight $1$ cuspform $f$ irregular at $p$ and having complex multiplication, and th…

math.NT2020★ 6 cited

Arithmetic of p-irregular modular forms: families and p-adic L-functions

Adel Betina, Chris Williams

Let $f_{new}$ be a classical newform of weight $\geq 2$ and prime to $p$ level. We study the arithmetic of $f_{new}$ and its unique $p$ -stabilisation $f$ when $f_…

math.NT2019

Geometry of the eigencurve at CM points and trivial zeros of Katz $p$ -adic $L$ -functions

Adel Betina, Mladen Dimitrov

The primary goal of this paper is to investigate the geometry of the $p$ -adic eigencurve at a point $f$ corresponding to a weight one cuspidal theta series irregular at the prime n…

math.NT2019

On Siegel eigenvarieties at Saito-Kurokawa points

Tobias Berger, Adel Betina

We study the geometry of the $p$ -adic Siegel eigenvariety $E$ of paramodular tame level at certain Saito-Kurokawa points having a critical slope. For $k \geq 2$ let $f$ b…

math.NT2018

On the Hilbert eigenvariety at exotic and CM classical weight 1 points

Adel Betina, Shaunak V. Deo, Francesc Fité

Let $F$ be a totally real number field and let $f$ be a classical cuspidal $p$ -regular Hilbert modular eigenform over $F$ of parallel weight $1$ . Let $x$ be the point on the $p$ -ad…

math.NT2018

On the failure of Gorensteinness at weight 1 Eisenstein points of the eigencurve

Adel Betina, Mladen Dimitrov, Alice Pozzi

We prove that the cuspidal eigencurve $C_{cusp}$ is étale over the weight space at any classical weight $1$ Eisenstein point $f$ and meets two Eisenstein components of the…

math.NT2017

Congruence formulae for Legendre modular polynomials

Adel Betina, Emmanuel Lecouturier

Let $p \geq 5$ be a prime number. We generalize the results of E. de Shalit about supersingular $j$ -invariants in characteristic $p$ . We consider supersingular elliptic curves with…

math.NT2016

On the $p$ -adic periods of the modular curve $X (Γ_{0} (p) \cap Γ (2))$

Adel Betina, Emmanuel Lecouturier

We prove a variant of Oesterlé's conjecture about $p$ -adic periods of the modular curve $X_{0} (p)$ , with an additional $Γ (2)$ -structure. We use de Shalit's techniques and $p$ -adic un…

math.NT2015★ 4 cited

Ramification of the eigencurve at classical RM points