Linear independence of even periods of modular forms. (English) Zbl 1534.11063
Summary: We show that if the dimension of the space of cuspforms is greater than or equal to three, then any three even periods are linearly independent. We also prove an asymptotic result for an arbitrary number of even periods. These results are achieved by studying the Rankin-Cohen brackets of Eisenstein series.
MSC:
| 11F30 | Fourier coefficients of automorphic forms |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11J72 | Irrationality; linear independence over a field |
References:
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