Determining cuspforms from critical values of convolution \(L\)-functions and Rankin-Cohen brackets. (English) Zbl 1456.11056
Summary: We show that a holomorphic newform \(g\) that is a Hecke eigenfunction can be uniquely determined by certain noncentral critical values of a family of convolution \(L\)-functions \(L(s, f \times g)\). The methods are different and simpler than those that use the central value to determine cuspforms.
MSC:
| 11F11 | Holomorphic modular forms of integral weight |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11F25 | Hecke-Petersson operators, differential operators (one variable) |
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