Overconvergent quaternionic forms and anticyclotomic p-adic L-functions

• Kim, Chan-Ho ^[1]
  1. [1] KIAS (Seül, Corea del Sud). School of Mathematics
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 63, Nº 2, 2019, págs. 727-767
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6321910
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• Resumen

  • We reinterpret the explicit construction of Gross points given by Chida-Hsieh as a non-Archimedian analogue of the standard geodesic cycle (i∞)-(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.