A new construction of \(p\)-adic Rankin convolutions in the case of positive slope. (English) Zbl 1267.11051
Summary: Given two newforms \(f\) and \(g\) of respective weights \(k\) and \(l\) with \(l<k\), Hida constructed a \(p\)-adic \(L\)-function interpolating the values of the Rankin convolution of \(f\) and \(g\) in the critical strip \(l \leq s \leq k\). However, this construction works only if \(f\) is an ordinary form. Using a method developed by Panchishkin to construct \(p\)-adic \(L\)-function associated with modular forms, we generalize this construction to the case where the slope of \(f\) is small.
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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