Derived Beilinson–Flach elements and the arithmetic of the adjoint of a modular form

Autor: Óscar Rivero, Victor Rotger

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Kings, Lei, Loeffler and Zerbes constructed in [LLZ], [KLZ1] a three-variable Euler system ¿(g,h) of Beilinson–Flach elements associated to a pair of Hida families (g,h) and exploited it to obtain applications to the arithmetic of elliptic curves,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f9c0ddfded18f0e8f659d1d542255163
https://doi.org/10.4171/jems/1054

On the rank and the convergence rate toward the Sato-Tate measure

Autor: Xavier Guitart, Francesc Fité

Publikováno v: International Mathematics Research Notices
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

Anstract. Let $A$ be an abelian variety defined over a number field and let $G$ denote its SatoTate group. Under the assumption of certain standard conjectures on $L$-functions attached to the irreducible representations of $G$, we study the converge

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ebf6d1949964160580430cbb7e464fa
http://hdl.handle.net/2445/193451

Stark points and the Hida-Rankin p-adic L-function

Autor: Daniele Casazza, Victor Rotger

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
The Ramanujan Journal
Recercat. Dipósit de la Recerca de Catalunya
instname

The final publication is available at Springer via http://dx.doi.org/10.1007/s11139-016-9824-y This article is devoted to the elliptic Stark conjecture formulated by Darmon (Forum Math Pi 3:e8, 2015), which proposes a formula for the transcendental p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13e0a3c7a6b4b938be7e87afef7e8013

Modular symbols

Autor: Gispert Sánchez, Francesc-Xavier

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

Modular forms are holomorphic functions defined on the complex upper half-plane which transform in a certain way under the action of a group of matrices. Alternatively, they can be thought of as differential forms on a Riemann surface known as a modu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::2a9a24ef0fb3f17ccfbfd77414d363ee
http://hdl.handle.net/2117/87420

Darmon points on elliptic curves over number fields of arbitrary signature

Autor: Xavier Guitart, Mehmet Haluk Sengun, Marc Masdeu

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 numerical evidence to support our conjecture.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5faaecd32a3a63f5e3a6eebb878063a4
http://wrap.warwick.ac.uk/129475/7/WRAP-Darmon-points-ellliptic-curves-number-arbitrary-Masdeu-2015.pdf