The exceptional zero conjecture for Hilbert modular forms

DOI10.1112/S0010437X08003813zbMath1247.11071WikidataQ123220229 ScholiaQ123220229MaRDI QIDQ3616540

Chung Pang Mok

Publication date: 25 March 2009

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4246840&fulltextType=RA&fileId=S0010437X08003813

zbMATH Keywords

Hilbert modular forms\(p\)-adic \(L\)-functionsexceptional zero conjecture

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items

ON THE QUATERNIONIC p-ADIC L-FUNCTIONS ASSOCIATED TO HILBERT MODULAR EIGENFORMS ⋮ \(p\)-adic \(L\)-functions of Hilbert cusp forms and the trivial zero conjecture ⋮ Derivative at \(s=1\) of the \(p\)-adic \(L\)-function of the symmetric square of an elliptic curve over a totally real field ⋮ Non-cuspidal Hida theory for Siegel modular forms and trivial zeros of \(p\)-adic \(L\)-functions ⋮ Overconvergent cohomology of Hilbert modular varieties and p-adic L-functions ⋮ On special zeros of \(p\)-adic \(L\)-functions of Hilbert modular forms ⋮ On Teitelbaum type \(\mathcal{L}\)-invariants of Hilbert modular forms attached to definite quaternions ⋮ Unnamed Item ⋮ Derivative at \(s = 1\) of the \(p\)-adic \(L\)-function of the symmetric square of a Hilbert modular form ⋮ The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication ⋮ Stark–Heegner cycles attached to Bianchi modular forms ⋮ EXCEPTIONAL ZEROES OF P-ADIC L-FUNCTIONS OVER NON-ABELIAN FIELD EXTENSIONS ⋮ Exceptional zeros and $\mathcal {L}$-invariants of Bianchi modular forms ⋮ Anticyclotomic 𝑝-adic 𝐿-functions and the exceptional zero phenomenon ⋮ On the \(p\)-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields ⋮ On Extra Zeros of p-Adic L-Functions: The Crystalline Case

Cites Work

• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• On Galois representations associated to Hilbert modular forms
• On \(L\)-functions of elliptic curves and cyclotomic towers
• On the Eisenstein series of Hilbert modular groups
• L-functions and division towers
• On p-adic Hecke algebras for \(GL_ 2\) over totally real fields
• On ordinary \(\lambda\)-adic representations associated to modular forms
• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• Values of abelian \(L\)-functions at negative integers over totally real fields
• On the factorization of p-adic L-series
• The special values of the zeta functions associated with Hilbert modular forms
• Motives for Hilbert modular forms
• \(p\)-adic \(L\)-functions of Hilbert modular forms
• Two variable \(p\)-adic \(L\) functions attached to eigenfamilies of positive slope
• \(p\)-adic \(L\)-functions and \(p\)-adic periods of modular forms
• CONVOLUTIONS OF HILBERT MODULAR FORMS AND THEIR NON-ARCHIMEDEAN ANALOGUES
• S -adic L -Functions Attached to the Symmetric Square of a Newform