Integration on Hp × H and arithmetic applications

By Henri Darmon. 2001

159 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0489aa7c1a71164c37c8bd6918c72f5c8c634218

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Citations in the corpus

Elliptic units for real quadratic fields (2006, methodology): “Some further explanation of the analogy (in the context of the Stark-Heegner points of [ Dar1 ]) can be found in Sections 4 and 5 of [BDG], and in the uniformization theory developed in [Das1], [Das3].”
On special zeros of p-adic L-functions of Hilbert modular forms (2012, background): “-invariant Lp(π) whenever pdoes not divide the discriminant of Dand we have πp ∼= St. These L-invariants have been deﬁned in the case F= Qand Ddeﬁnite by Teitelbaum [Te], for F= Q, D= M2(Q) by Darmon [Da] (for weight 2) and Orton [Or] (higher even weight) and if Fhas narrow class number 1 by Greenbe”
Shintani zeta functions and Gross-Stark units for totally real fields (2008, methodology): “The case where F is real quadratic and H is a ring class field extension was addressed in [7], where a formula for Stark’s unit was proposed using modular symbols in analogy with Darmon’s definition of Stark–Heegner points [6].”
$p$-adic $L$-functions and unitary completions of representations of $p$-adic reductive groups (2005, methodology): “As an application, we prove a version of the Mazur-Tate-Teitelbaum exceptional zero conjecture [16, p. 46], using the representation theoretic definition of the L-invariant given by Breuil in [5] (which provides a reinterpretation of the definition given by Darmon [9] and Orton [18] in the weight tw”
STARK-HEEGNER POINTS AND THE COHOMOLOGY OF QUATERNIONIC SHIMURA VARIETIES (2009, methodology): “Darmon’s idea in [5] is to construct points in E(Kab) by replacing the archimedean analysis present in the classical Heegner point construction with p-adic analysis.”