Pullback formula for vector valued Siegel modular forms and its\n applications

2021/09/24 by Noritomo Kozima, Kozima, Noritomo · 1 citation
Mathematics · #11F46 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.11753

openalex publication_date 2021/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E_n be the Siegel Eisenstein series of degree n and weight k with a\ncomplex parameter s. In this paper, using a differential operator D by\nIbukiyama which sends a scalar valued Siegel modular form to the tensor product\nof two vector valued Siegel modular forms, under a certain condition, we give a\nformula of DE_p+q on H_p\× H_q, where H_n is the Siegel upper half\nspace of degree n. Furthermore, we give some applications of this formula,\ni.e., analytic properies of standard L-functions and the Klingen Eisenstein\nseries and algebraicity results for Siegel modular forms and standard\nL-functions.\n

Cited by

• Differential operators on Hermitian modular forms on U(n, n)

Related

• Pullbacks of Siegel Eisenstein Series and Weighted Averages of Critical L-values
• Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)
• On the Rankin-Selberg method for vector valued Siegel modular forms
• Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series
• Eisenstein series identities based on partial fraction decomposition