共查询到20条相似文献,搜索用时 15 毫秒
1.
Jo?l Bella?che 《Inventiones Mathematicae》2012,189(1):1-60
We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve. 相似文献
2.
Michael Spieß 《Inventiones Mathematicae》2014,196(1):69-138
Let E be a modular elliptic curve over a totally real number field F. We prove the weak exceptional zero conjecture which links a (higher) derivative of the p-adic L-function attached to E to certain p-adic periods attached to the corresponding Hilbert modular form at the places above p where E has split multiplicative reduction. Under some mild restrictions on p and the conductor of E we deduce the exceptional zero conjecture in the strong form (i.e. where the automorphic p-adic periods are replaced by the $\mathcal {L}$ -invariants of E defined in terms of Tate periods) from a special case proved earlier by Mok. Crucial for our method is a new construction of the p-adic L-function of E in terms of local data. 相似文献
3.
Yi Wen DING 《数学学报(英文版)》2021,37(1):121-141
We study the adjunction property of the Jacquet–Emerton functor in certain neighborhoods of critical points in the eigencurve. As an application, we construct two-variable p-adic L-functions around critical points via Emerton's representation theoretic approach. 相似文献
4.
Inventiones mathematicae - 相似文献
5.
Daqing Wan 《Inventiones Mathematicae》1998,133(2):449-463
A quadratic bound is obtained for a conjecture of Gouvêa-Mazur on arithmetic variation of dimensions of classical and p-adic modular forms.
Oblatum 22-VIII-1996 & 8-X-1997 相似文献
6.
L.C Washington 《Journal of Number Theory》1976,8(2):245-250
An elementary proof is given for the existence of the Kubota-Leopoldt p-adic L-functions. Also, an explicit formula is obtained for these functions, and a relationship between the values of the p-adic and classical L-functions at positive integers is discussed. 相似文献
7.
We give a sufficient condition, namely “Buzzard irregularity”, for there to exist a cuspidal eigenform which does not have integral p-adic slope. 相似文献
8.
Inventiones mathematicae - 相似文献
9.
The Ramanujan Journal - In this paper we study the Mahler measures of two families of Laurent polynomials. We prove several three-variable Mahler measure formulas initially conjectured by D. Samart. 相似文献
10.
Atsushi Murase 《Mathematische Annalen》2010,347(3):529-543
Let f be a holomorphic cusp form of weight l on SL2(Z) and Ω an algebraic Hecke character of an imaginary quadratic field K with Ω((α)) = (α/|α|) l for ${\alpha\in K^{\times}}Let f be a holomorphic cusp form of weight l on SL2(Z) and Ω an algebraic Hecke character of an imaginary quadratic field K with Ω((α)) = (α/|α|)
l
for a ? K×{\alpha\in K^{\times}}. Let L(f, Ω; s) be the Rankin-Selberg L-function attached to (f, Ω) and P(f, Ω) an “Ω-averaged” sum of CM values of f. In this paper, we give a formula expressing the central L-values L(f, Ω; 1/2) in terms of the square of P(f, Ω). 相似文献
11.
Bei Zhang 《Journal of Number Theory》2011,131(3):419-439
In this paper, I discuss the construction of the p-adic L-function attached to a Hilbert modular form f, supersingular or ordinary, which turns out to be the non-archimedean Mellin transform of an h-admissible measure. And h is explicitly given. As a special case, when the Fourier coefficient of f at p|p is zero, plus/minus p-adic L-functions are furthermore defined as bounded functions, and they interpolate special values of L(f,χ,s) for cyclotomic characters χ. This can be used to formulate Iwasawa main conjecture for supersingular elliptic curve defined over a totally real field. 相似文献
12.
In this paper p-adic analogs of the Lichtenbaum Conjectures are proven for abelian number fields F and odd prime numbers p, which generalize Leopoldt's p-adic class number formula, and express special values of p-adic L-functions in terms of orders of K-groups and higher p-adic regulators. The approach uses syntomic regulator maps, which are the p-adic equivalent of the Beilinson regulator maps. They can be compared with étale regulators via the Fontaine-Messing map,
and computations of Bloch-Kato in the case that p is unramified in F lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters.
Oblatum 14-V-96 & 9-X-97 相似文献
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14.
Tsuneo Arakawa 《manuscripta mathematica》1983,44(1-3):155-185
In [1], [2], Andrianov constructed a remarkable Hecke theory for Siegel's modular forms of degree two. In this article we extend some of his results to the case of vector valued Siegel's modular forms of degree two. 相似文献
15.
The Ramanujan Journal - Previous works have shown that certain weight 2 newforms are p-adic limits of weakly holomorphic modular forms under repeated application of the U-operator. The proofs of... 相似文献
16.
We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We
also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we
investigate the effect of adding an assumption of periodicity to this criterion.
2000 Mathematics Subject Classification Primary—11F12, 11F66
G. Mason: Research supported in part by NSF Grant DMS 0245225.
C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34. 相似文献
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We give a new expression for the inner product of two kernel functions associated to a cusp form. Among other applications,
it yields an extension of a formula of Kohnen and Zagier, and another proof of Manin’s Periods Theorem. Cohen’s representation
of these kernels as series is also generalized. 相似文献