哈德猜想1

Pub Date : 2021-09-22 DOI:10.2969/jmsj/87988798

Hiraku Atobe, Masataka Chida, T. Ibukiyama, H. Katsurada, Takuya Yamauchi

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引用次数: 2

摘要

设$f$是关于$SL_2（Z）$的基元形式。然后，我们提出了关于$f$的Duke Imamoglu Ikeda提升的Klingen-Eisenstein提升与向量值Hecke本征形式关于$Sp_2（Z）$的某个提升之间的一致性的猜想。这个猜想暗示了哈德猜想。我们在某些情况下证明了上述猜想。

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Harder's conjecture I

Let $f$ be a primitive form with respect to $SL_2(Z)$. Then we propose a conjecture on the congruence between the Klingen-Eisenstein lift of the Duke-Imamoglu-Ikeda lift of $f$ and a certain lift of a vector valued Hecke eigenform with respect to $Sp_2(Z)$. This conjecture implies Harder's conjecture. We prove the above conjecture in some cases.

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