STARK POINTS AND -ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE
نویسندگان
چکیده
منابع مشابه
STARK POINTS AND p-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE
Let E be an elliptic curve over Q, and let %[ and %] be odd two-dimensional Artin representations for which %[ ⊗ %] is self-dual. The progress on modularity achieved in recent decades ensures the existence of normalized eigenforms f , g, and h of respective weights two, one, and one, giving rise to E , %[, and %] via the constructions of Eichler and Shimura, and of Deligne and Serre. This artic...
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This article can be read as a companion and sequel to [DLR], which proposes a conjectural expression for the so-called p-adic iterated integrals attached to a triple (f, g, h) of classical eigenforms of weights (2, 1, 1). When f is a cusp form, this expression involves the p-adic logarithms of so-called Stark points: distinguished points on the modular abelian variety attached to f , defined ov...
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The decomposition into an Euler product and the functional equation of the Dirichlet series associated by Hecke to modular forms of weight one suggests that these correspond to Artin L-functions of degree 2 over Q, otherwise known as Galois representations Gal(Q/Q)→ GL2(C). It is this correspondence, conjectured by Langlands, which we establish here. The first three sections are preliminary. Th...
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The p-adic interpolation of modular forms on congruence subgroups of SL2(Z) has been succesfully used in the past to interpolate values of L-series. In [12], Serre interpolated the values at negative integers of the ζ-series of a totally real number field (in fact of L-series of powers of the Teichmuller character) by interpolating Eisenstein series, which are holomorphic modular forms, and loo...
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ژورنال
عنوان ژورنال: Forum of Mathematics, Pi
سال: 2015
ISSN: 2050-5086
DOI: 10.1017/fmp.2015.7