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- W2344975449 abstract "A major theme in the theory of p-adic deformations of automorphic forms is how p-adic L-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this article we prove results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We show that the crossing of two Hida families is determined by the local behavior of p-adic L-functions on those Hida families. In addition, we prove that the local behavior of p-adic L-functions determines when a Hida family ramifies over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special L-values and then p-adically interpolating congruences." @default.
- W2344975449 created "2016-06-24" @default.
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- W2344975449 date "2022-07-07" @default.
- W2344975449 modified "2023-10-18" @default.
- W2344975449 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>p</mml:mi></mml:math>-adic<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>L</mml:mi></mml:math>-functions and the geometry of Hida families" @default.
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- W2344975449 doi "https://doi.org/10.5802/aif.3467" @default.
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