An explicit formula for Siegel series

Abstract

Combining induction formulas for local densities with a functional equation for the Siegel series, we give an explicit formula for the Siegel series. By this formula, we also give an explicit formula for the Fourier coefficients of the Siegel Eisenstein series.

Linear relations between Fourier coefficients of special Siegel modular forms

“…6]). Note that (6) also follows easily from certain recursion formulas for the local singular series polynomials given in [6], cf. in particular [6; Thm.…”

Fourier coefficients of degree two Siegel–Eisenstein series with trivial character at squarefree level

“…(first degree 3 [7,9], then any degree [8]) and Kohnen (even degree [10]), ChoieKohnen (odd degree [2]). Katsurada's approach has more in common with Maass' approach, whereas Kohnen's approach (for even degree) is at least nominally closer to that of Eichler-Zagier with his linearised version of the Ikeda lift playing a rôle simlar to the Maass lift.…”

On p-adic Siegel–Eisenstein series of weight k

“…For any integer k > 3 such that k ≡ (p − 1)/2 (mod 2), a Siegel-Eisenstein series E (2) k,χ p of degree two, weight k and character χ p on Γ (2) 0 (p) is defined in the standard way as E…”

“…0 (p), χ p ), the space of all Siegel modular forms of degree two, weight k and character χ p on Γ (2) 0 (p). The following identity will be proved in Section 3.…”

“…0 (p), χ p ) and thus various explicit formulas for local densities of quadratic forms [2], [6] were needed. One can think that the use of E (2) k,χ p is rather natural.…”