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Searching for \(p\)-adic eigenfunctions. (English) Zbl 0851.11031

Let \(U\) denote the Atkin operator. The authors propose a computational procedure to search for nonclassical overconvergent \(p\)-adic \(U\)-eigenforms. The idea is to approximate the \(p\)-adic \(U\)-eigenfunction expansion which eventually may produce a candidate Fourier expansion. They use the asymptotic \(U\)-spectral expansion to give concrete examples for \(p = 5,3\).

MSC:

11F33 Congruences for modular and \(p\)-adic modular forms
11F30 Fourier coefficients of automorphic forms
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