4,808 research outputs found
A control theorem for -adic automorphic forms and Teitelbaum's -invariant
In this article, we describe an efficient method for computing Teitelbaum's
-adic -invariant. These invariants are realized as the
eigenvalues of the -operator acting on a space of harmonic
cocycles on the Bruhat-Tits tree , which is computable by the
methods of Franc and Masdeu described in \cite{fm}. The main difficulty in
computing the -operator is the efficient computation of the
-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 -adic automorphic forms of arbitrary even weight.
Moreover, we give computational evidence for relations between slopes of
-invariants of different levels and weights for .Comment: 26 page
On the Twisted q-Euler numbers and polynomials associated with basic q-l-functions
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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