Abstract
Let $f$ be a primitive form with respect to $\mathrm{SL}_{2}(\mathbb{Z})$. 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 $\mathrm{Sp}_{2}(\mathbb{Z})$. This conjecture implies Harder's conjecture. We prove the above conjecture in some cases.
Funding Statement
The first author was supported by JSPS KAKENHI Grant Number JP19K14494. The second author was supported by JSPS KAKENHI Grant Number JP18K03202. The third author was supported by JSPS KAKENHI Grant Number JP19K03424, JP20H00115. The fourth author was supported by KAKENHI Grant Number JP16H03919, JP21K03152. The fifth author was supported by JSPS KAKENHI Grant Number JP19H01778.
Citation
Hiraku ATOBE. Masataka CHIDA. Tomoyoshi IBUKIYAMA. Hidenori KATSURADA. Takuya YAMAUCHI. "Harder's conjecture I." J. Math. Soc. Japan 75 (4) 1339 - 1408, October, 2023. https://doi.org/10.2969/jmsj/87988798
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