A Shimura-Shintani correspondence for rigid analytic cocycles of higher weight

DOI10.1515/FORUM-2022-0235arXiv2208.05903MaRDI QIDQ6407637

Isabella Negrini

Publication date: 11 August 2022

Abstract: This paper takes the first steps towards a systematic study of additive rigid meromorphic cocycles of higher weight. These were introduced by Darmon and Vonk, who focused on multiplicative and weight two cocycles. After classifying certain rigid meromorphic cocycles of weight $2k$, we construct an explicit holomorphic kernel function realising a Shimura-Shintani style correspondence from modular forms of weight $k+1/2$ and level $4p^2$ to rigid analytic cocycles of weight $2k$ on SL${}_2(mathbbZ[1/p])$.

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) (p)-adic theory, local fields (11F85) Complex multiplication and moduli of abelian varieties (11G15)

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