Moments of ideal class counting functions. (English) Zbl 07802060
Summary: We consider the counting function of ideals in a given ideal class of a number field of degree \(d\). This describes, at least conjecturally, the Fourier coefficients of an automorphic form on \(\mathrm{GL}(d)\), typically not a Hecke eigenform and not cuspidal. We compute its moments, and also investigate the moments of the corresponding cuspidal projection.
MSC:
| 11N37 | Asymptotic results on arithmetic functions |
| 11R42 | Zeta functions and \(L\)-functions of number fields |
| 11F30 | Fourier coefficients of automorphic forms |
| 20C15 | Ordinary representations and characters |
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