Recursion formulas for the Fourier coefficients of Siegel Eisenstein series of an odd prime level

2025/04/24 by Keiichi Gunji, Gunji, Keiichi
Mathematics · #11F30 (Primary) #11F46(Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.17245

openalex publication_date 2025/04/24 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

In this paper we treat the Fourier coefficients of Siegel Eisenstein series of level p with trivial or quadratic character, for an odd prime p. The Euler p-factor of the Fourier coefficient is called the ramified Siegel series. First we show that the ramified Siegel series attached to each cusp can be decomposed to U(p)-eigenfunctions explicitly, next we give recursion formulas of such U(p)-characteristic ramified Siegel series.

Related

• On the functional equations of Siegel Eisenstein series of an odd prime level p
• On the calculation of the ramified Siegel series
• On Siegel--Eisenstein series of level p and their p-adic properties
• Multiplicative relations for Fourier coefficients of degree 2 Siegel\n eigenforms
• On the rationality of a paramodular Siegel Eisenstein series