On the non-vanishing of Fourier coefficients of half-integral weight cuspforms. (English) Zbl 1540.11041
Summary: We prove the best possible upper bounds of the gaps between non-vanishing Fourier coefficients of half-integral weight cuspforms. This improves the works of A. Balog and K. Ono [J. Number Theory 91, No. 2, 356–371 (2001; Zbl 1016.11053)] and J. Thorner [Math. Proc. Camb. Philos. Soc. 161, No. 1, 53–63 (2016; Zbl 1371.11133)]. We also show an asymptotic formula of central modular \(L\)-values for short intervals.
MSC:
| 11F30 | Fourier coefficients of automorphic forms |
| 11F11 | Holomorphic modular forms of integral weight |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
References:
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