An explicit comparison of anticyclotomic p-adic L-functions for Hida families

DOI10.1142/s1793042123500987arXiv2205.08080OpenAlexW4364360237MaRDI QIDQ6050853

Matteo Longo, Chan-Ho Kim

Publication date: 19 September 2023

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.08080

zbMATH Keywords

Iwasawa theoryanticyclotomic \(p\)-adic \(L\)-functions\(p\)-adic families of modular forms

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Cites Work

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• Big Heegner points and special values of \(L\)-series
• Mazur-Tate elements of nonordinary modular forms
• Quaternion algebras, Heegner points and the arithmetic of Hida families
• Anticyclotomic \(p\)-ordinary Iwasawa theory of elliptic modular forms
• Iwasawa's main conjecture for elliptic curves over anticyclotonic \(\mathbb Z_p\)-extensions
• Variation of Heegner points in Hida families
• A p-adic measure attached to the zeta functions associated with two elliptic modular forms. I
• A \(p\)-adic measure attached to the zeta functions associated with two elliptic modular forms. II
• Periods of Hecke characters
• On the periods of modular forms
• Special values of anticyclotomic \(L\)-functions for modular forms
• Anticyclotomic Iwasawa invariants and congruences of modular forms
• Variation of anticyclotomic Iwasawa invariants in Hida families
• Special values of anticyclotomic \(L\)-functions.
• Canonical periods and congruence formulae
• Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\)
• The \(p\)-adic variation of the Gross-Kohnen-Zagier theorem
• Rankin-Eisenstein classes and explicit reciprocity laws
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Central derivatives of \(L\)-functions in Hida families
• Automorphic forms on \(\mathrm{GL}(2)\). Part II
• On anticyclotomic μ-invariants of modular forms
• Euler systems for modular forms over imaginary quadratic fields
• Modules of Congruence of Hecke Algebras and L-Functions Associated with Cusp Forms
• Fonctions L p -Adiques Associees a Une Forme Modulaire Et a Un Corps Quadratique Imaginaire
• The special values of the zeta functions associated with cusp forms
• Hida families and p-adic triple product L-functions
• Vanishing of special values and central derivatives in Hida families
• Modular Forms
• Heegner points on Mumford-Tate curves
• Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg \(L\)-values in Hida families