Let f ∈ Sk0+2(Γ0(Np)) be a normalized N-new eigenform with p ∤ N and such that ap2 ≠ pk0+1 and ordp(ap) < k0 + 1. By Coleman's theory, there is a p-adic family of eigenforms whose weight k0 + 2 specialization is f. Let K be a real quadratic field and let ψ be an unramified character of Gal(K̅ /K). Under mild hypotheses on the discriminant of K and the factorization of N, we construct a p-adic L-function ℒ/K,ψ interpolating the central critical values of the Rankin L-functions associated to the base change to K of the specializations of in classical weight, twisted by ψ. When the character ψ is quadratic, ℒ/K,ψ factors into a product of two Mazur-Kitagawa p-adic L-functions. If, in addition, has p-new specialization in weight k0 + 2, then under natural parity hypotheses we may relate derivatives of each of the Mazur-Kitagawa factors of ℒ/K,ψ at k0 to Bloch–Kato logarithms of Heegner cycles. On the other hand the derivatives of our p-adic L-functions encodes the position of the so called Darmon cycles.
Modular p-adic L-functions attached to real quadratic fields and arithmetic applications / M. Greenberg, M.A. Seveso, S. Shahabi. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 721(2016), pp. 167-231. [10.1515/crelle-2014-0088]
Modular p-adic L-functions attached to real quadratic fields and arithmetic applications
M.A. SevesoSecondo
;
2016
Abstract
Let f ∈ Sk0+2(Γ0(Np)) be a normalized N-new eigenform with p ∤ N and such that ap2 ≠ pk0+1 and ordp(ap) < k0 + 1. By Coleman's theory, there is a p-adic family of eigenforms whose weight k0 + 2 specialization is f. Let K be a real quadratic field and let ψ be an unramified character of Gal(K̅ /K). Under mild hypotheses on the discriminant of K and the factorization of N, we construct a p-adic L-function ℒ/K,ψ interpolating the central critical values of the Rankin L-functions associated to the base change to K of the specializations of in classical weight, twisted by ψ. When the character ψ is quadratic, ℒ/K,ψ factors into a product of two Mazur-Kitagawa p-adic L-functions. If, in addition, has p-new specialization in weight k0 + 2, then under natural parity hypotheses we may relate derivatives of each of the Mazur-Kitagawa factors of ℒ/K,ψ at k0 to Bloch–Kato logarithms of Heegner cycles. On the other hand the derivatives of our p-adic L-functions encodes the position of the so called Darmon cycles.File | Dimensione | Formato | |
---|---|---|---|
Modular p-adic L-functions attached to real quadratic fields and arithmetic applications.pdf
accesso aperto
Descrizione: Articolo principale
Tipologia:
Pre-print (manoscritto inviato all'editore)
Dimensione
672.2 kB
Formato
Adobe PDF
|
672.2 kB | Adobe PDF | Visualizza/Apri |
[14355345 - Journal für die reine und angewandte Mathematik] Modular p-adic L-functions attached to real quadratic fields_and arithmetic applications.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
734.66 kB
Formato
Adobe PDF
|
734.66 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.