Open Access
2019 Overconvergent Quaternionic Forms and Anticyclotomic $p$-adic $L$-functions
Chan-Ho Kim
Publ. Mat. 63(2): 727-767 (2019). DOI: 10.5565/PUBLMAT6321910


We reinterpret the explicit construction of Gross points given by Chida-Hsieh as a non-Archimedian analogue of the standard geodesic cycle $(i\infty) - (0)$ on the Poincaré upper half plane. This analogy allows us to consider certain distributions, which can be regarded as anticyclotomic $p$-adic $L$-functions for modular forms of non-critical slope following the overconvergent strategy à la Stevens. We also give a geometric interpretation of their Gross points for the case of weight two forms. Our construction generalizes those of Bertolini-Darmon, Bertolini-Darmon-Iovita-Spiess, and Chida-Hsieh and shows a certain integrality of the interpolation formula even for non-ordinary forms.


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Chan-Ho Kim. "Overconvergent Quaternionic Forms and Anticyclotomic $p$-adic $L$-functions." Publ. Mat. 63 (2) 727 - 767, 2019.


Received: 20 December 2017; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07094868
MathSciNet: MR3980939
Digital Object Identifier: 10.5565/PUBLMAT6321910

Primary: 11R23
Secondary: 11F33

Keywords: $p$-adic $L$-functions , automorphic forms , Gross points , Iwasawa theory , quaternion algebras

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 2 • 2019
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