Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series

2011/10/12 by Lynne H. Walling, Walling, Lynne H.
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1110.2797

openalex publication_date 2011/10/12 · arxiv created 2011/10/17 · arxiv updated 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We evaluate the action of Hecke operators on Siegel Eisenstein series of degree 2, square-free level and arbitrary character, without using knowledge of their Fourier coefficients. From this we construct a basis of simultaneous eigenforms for the full Hecke algebra, and we compute their eigenvalues. As well, we obtain Hecke relations among the Eisenstein series. Using these Hecke relations in the case that \stufe is square-free and the character is trivial, we generate a basis for the space of Eisenstein series.

Related

• Hecke operators on half-integral weight Siegel Eisenstein series
• Hecke eigenvalues of Klingen--Eisenstein series of squarefree level
• Multiplicative relations for Fourier coefficients of degree 2 Siegel\n eigenforms
• Action of Hecke operators on Siegel theta series II
• Some relations on Fourier coefficients of degree 2 Siegel forms of\n arbitrary level