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A new method of constructing \(p\)-adic \(L\)-functions associated with modular forms. (English) Zbl 1011.11026
The author gives a new method of constructing \(p\)-adic measures associated with modular forms. He starts from distributions with values in spaces of modular forms (holomorphic or nearly holomorphic) and uses the canonical operator onto the primary subspace associated to a nonzero eigenvalue of the Atkin-Lehner operator. The construction does not use any \(p\)-adic limit procedure. Both \(p\)-ordinary and \(p\)-supersingular cases can be treated by this method. Examples include classical \(p\)-adic measures attached to modular forms and triple product \(L\)-functions.

MSC:
11F33 Congruences for modular and \(p\)-adic modular forms
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F30 Fourier coefficients of automorphic forms
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