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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.
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참고문헌 (9)
참고문헌 신청
B. C. Berndt / 1998 / Gauss and Jacobi Sums, Canadian Mathematical Society Series of Monographs and Advanced Texts / John Wiley & Sons, Inc
J. H. Bruinier / 2002 / Borcherds products on O(2, l) and Chern classes of Heegner divisors / Springer-Verlag
Jan Hendrik Bruinier / 2004 / On two geometric theta lifts / Duke Mathematical Journal 125(1):45~90
Jan Hendrik Bruinier / 2001 / Eisenstein series attached to lattices¶and modular forms on orthogonal groups / manuscripta mathematica 106(4):443~459
J. H. Conway / 1999 / Sphere packings, lattices and groups / Springer-Verlag
J. H. Bruinier / 2002 / Borcherds products on O(2, l) and Chern classes of Heegner divisors / Springer-Verlag
Jan Hendrik Bruinier / 2004 / On two geometric theta lifts / Duke Mathematical Journal 125(1):45~90
Jan Hendrik Bruinier / 2001 / Eisenstein series attached to lattices¶and modular forms on orthogonal groups / manuscripta mathematica 106(4):443~459
J. H. Conway / 1999 / Sphere packings, lattices and groups / Springer-Verlag
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