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On a sufficient condition for the existence of admissible \(p\)-adic measures. (Sur une condition suffisante pour l’existence de mesures \(p\)-adiques admissibles.) (French) Zbl 1078.11038

The author gives a new sufficient condition for the existence of admissible \(p\)-adic measures obtained from sequences of distributions \((\Phi_j)_{i\geq 0}\) with values in spaces of modular forms (Theorem 1). The condition is expressed in terms of congruences between Fourier coefficients of modular forms \(\Phi_j\). The author verifies these congruences in the classical cases of Rankin-Selberg convolutions and triple product \(L\)-functions (sections 9 and 10).

MSC:

11F85 \(p\)-adic theory, local fields
11F33 Congruences for modular and \(p\)-adic modular forms
11F30 Fourier coefficients of automorphic forms
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References:

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