AUTOMORPHIC FORMS ON THE COMPLEX AND REAL BALLS DERIVED FROM THETA CONSTANTS

MATSUMOTO Keiji

doi:10.2206/kyushujm.58.71

AUTOMORPHIC FORMS ON THE COMPLEX AND REAL BALLS DERIVED FROM THETA CONSTANTS

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MATSUMOTO Keiji

Division of Mathematics Graduate School of Science Hokkaido University

書誌事項

公開日: 2004

DOI

10.2206/kyushujm.58.71

公開者: 九州大学大学院数理学研究院

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説明

Through the modular embedding of the complex n-dimensional ball Bⁿ_C into the Siegel upper half-space Sⁿ⁺¹ of degree n + 1 with respect to the Eisenstein integers Z[ω], we pull back the theta constants on Sⁿ⁺¹. We find a condition on the characteristics of the theta constants so that the pullbacks are non-zero automorphic forms on Bⁿ_C with respect to the congruence subgroup Γ(1−ω). These automorphic forms are real valued on the real ball naturally embedded in the complex ball.