4,808 research outputs found

    A control theorem for pp-adic automorphic forms and Teitelbaum's L\mathcal{L}-invariant

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    In this article, we describe an efficient method for computing Teitelbaum's pp-adic L\mathcal{L}-invariant. These invariants are realized as the eigenvalues of the L\mathcal{L}-operator acting on a space of harmonic cocycles on the Bruhat-Tits tree T\mathcal{T}, which is computable by the methods of Franc and Masdeu described in \cite{fm}. The main difficulty in computing the L\mathcal{L}-operator is the efficient computation of the pp-adic Coleman integrals in its definition. To solve this problem, we use overconvergent methods, first developed by Darmon, Greenberg, Pollack and Stevens. In order to make these methods applicable to our setting, we prove a control theorem for pp-adic automorphic forms of arbitrary even weight. Moreover, we give computational evidence for relations between slopes of L\mathcal{L}-invariants of different levels and weights for p=2p=2.Comment: 26 page

    On the Twisted q-Euler numbers and polynomials associated with basic q-l-functions

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    One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler numbers and polynomials.Comment: 8 page
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