Critical slope p-adic L-functions of CM modular forms
نویسندگان
چکیده
منابع مشابه
Iwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions
We construct an Euler system of p-adic zeta elements over the eigencurve which interpolates Kato’s zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable p-adic L-function over the eigencurve. As a first application of these ideas, we prove the equality of the p-adic L-functions associated with a critical-slope refin...
متن کاملCritical slope p-adic L-functions
Let g be an eigenform of weight k+2 on Γ0(p)∩Γ1(N) with p N . If g is non-critical (i.e. of slope less than k + 1), using the methods of [1, 20], one can attach a p-adic L-function to g which is uniquely determined by its interpolation property together with a bound on its growth. However, in the critical slope case, the corresponding growth bound is too large to uniquely determine the p-adic L...
متن کاملCRITICAL SLOPE p-ADIC L-FUNCTIONS – DRAFT
Let p be a prime number, and let f = ∑ n anq n denote a normalized cuspidal eigenform of weight k + 2 on Γ0(N) with p N . If f is a p-ordinary form, then by [1, 17] we can attach a p-adic L-function to f which interpolates special values of its L-series. On the other hand, if f is non-ordinary at p, we have two p-adic L-functions attached to f , one for each root of x − apx + p. These two roots...
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Let E be an elliptic curve which is defined over Q and has stable reduction modulo a given prime p. Assuming that E is modular, one can associate to E a p-adic L-function Lp(E, s). (See [-Mz-SwD, A-V, Vi, Mz-T-T] for its construction in various cases.) This function is defined by a certain interpolation property and is analytic for seZp. In this paper, we will assume that E has split multiplica...
متن کاملMOCK MODULAR FORMS AS p-ADIC MODULAR FORMS
In this paper, we consider the question of correcting mock modular forms in order to obtain p-adic modular forms. In certain cases we show that a mock modular form M is a p-adic modular form. Furthermore, we prove that otherwise the unique correction of M is intimately related to the shadow of M.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2013
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-013-0020-0