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

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概要

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• Through the modular embedding of the complex $ n $-dimensional ball $ \mathbb{{B}_{C} ^{n}} $ into the Siegel upper half-space $ \mathbb{S^{n+1}} $ of degree $ n+1 $ with respect to the Eisenstein integers $ \mathbb{Z}[ \omega ] $, we pull back the theta constants on $ \mathbb{S}^{n+1} $. We find a condition on the characteristics of the theta constants so that the pullbacks are non-zero automorphic forms on $ \mathbb{B_{C} ^{n}} $ with respect to the congruence subgroup $ \Gamma (1- \omega ) $. These automorphic forms are real valued on the real ball naturally embedded in the complex ball.

• Faculty of Mathematics, Kyushu Universityの論文

著者

• Matsumoto Keiji

  Division Of Mathematics Graduate School Of Science Hokkaido University

関連論文

• Theta Constants Associated with the Cyclic Triple Coverings of the Complex Projective Line Branching at Six Points
• AUTOMORPHIC FORMS ON THE COMPLEX AND REAL BALLS DERIVED FROM THETA COSTANTS

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