Fourier coefficients of Eisenstein series on \rm SO(3,n+1)

2025/12/03 by Henry H. Kim, Kim, Henry H., Takuya Yamauchi +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2512.03412

Abstract

We explicitly compute Fourier coefficients of Eisenstein series on the special orthogonal group G=\rm SO(3,n+1) over ℚ with n≥ 2 which splits everywhere at finite places. We show that it has a bounded denominator.

Citations

• Theta lifts to certain cohomological representations of indefinite orthogonal groups
• Arthur's multiplicity formula for even orthogonal and unitary groups
• Modular forms on indefinite orthogonal groups of rank three
• The minimal modular form on quaternionic E₈
• On the functional equation of the Siegel series
• Higher level cusp forms on the exceptional group of type E₇

Related

• Higher level cusp forms on the exceptional group of type E₇
• Period of the Ikeda type lift for E_7,3
• Ikeda's conjecture on the period of the Duke-Imamoglu-Ikeda lift
• Non-vanishing of Miyawaki type lift
• Congruence between Duke-Imamoglu-Ikeda lifts and non-Duke-Imamoglu-Ikeda lifts