2024/04/19 by Isabella Negrini, Negrini, Isabella
Engineering · #11 #FOS: Mathematics #Number Theory (math.NT) #Power Systems and Technologies #Railway Systems and Energy Efficiency #Real-time simulation and control systems
paper · pdf · doi:10.48550/arxiv.2404.12936
openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a Shintani lift for rigid analytic cocycles of higher weight, attaching modular forms of half-integral weight to such cocycles. The expression for the Fourier coefficients of the modular form RS(J) attached to a cocycle J is given in terms of the residues of J, and shares a striking similarity with the expression for the coefficients of the classical Shintani lift S(f) of an integral weight modular form f. This work aligns with the ideas of the nascent p-adic Kudla program and strengthens the analogy between rigid cocycles and modular forms.