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Showing 1 to 6 of 6 for “"p-adic L-function"”.
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On Selmer groups and factoring p-adic L-functions
… restriction of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and a Kubota-Leopoldt p-adic L-function. We prove a result involving Selmer groups that along with Dasgupta's result is consistent …
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p-adic L-functions of automorphic forms
… at places above p and ∞) we construct a p-adic L-function which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization of a construction by Spieß over totally real fields. It seems well-suited to generalize his proof of the …
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Iwasawa theory for tensor products of Hilbert modular forms
… it provides a deep connection between the p-adic L-function which interpolates critical values of the complex L-series, and the Selmer group which is an important object used to control the growth of arithmetic data. In this thesis, we explore some questions that arise organically from the …
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Zeros of P-Adic L-Functions and Densities Relating to Bernoulli Numbers
… p < 125,000 it is known that the corresponding p-adic L-function L(,p)(s,(chi)(,i)) of Kubota and Leopoldt has a unique zero ('i)(kappa) in the p-adic integers. For every irregular pair (p,i) with p < 1000, several p-adic places of ('i)(kappa) are calculated using a p-adic Newton's method and the …
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… objects (motives) and the special values of L-functions. A precise form of this relationship is neatly encoded in the so-called "Iwasawa Main Conjecture". Classically the Main Conjecture (as formulated by Iwasawa himself) involved the behaviour of ideal class groups over cyclotomic …
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
… twists, we establish a lower bound for the $2$-adic valuation of the algebraic part of the complex $L$-series at $s=1$, and, for the family of cubic twists, we establish a lower bound for the $3$-adic valuation of the algebraic part of the same $L$-value. We show that our lower bounds are …