A note on vector-valued Eisenstein series of weight $3/2$
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Vector-valued Eisenstein series of weight $3/2$ are often not holomorphic. In this paper we prove that, for an even lattice $\lat L$, if there exists an odd prime $p$ such that $\lat L$ is local $p$-maximal and the determinant of $\lat L$ is divisible by $p^{2}$, then the Eisenstein series of weight $3/2$ attached to the discriminant form of $\lat L$ is holomorphic.
Abstract
Vector-valued Eisenstein series of weight $3/2$ are often not holomorphic. In this paper we prove that, for an even lattice $\lat L$, if there exists an odd prime $p$ such that $\lat L$ is local $p$-maximal and the determinant of $\lat L$ is divisible by $p^{2}$, then the Eisenstein series of weight $3/2$ attached to the discriminant form of $\lat L$ is holomorphic.
참고문헌 (9)
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