Shimura Lifts of Nearly Holomorphic Modular Forms

Key Points

• The research aims to extend Shimura lifts to nearly holomorphic modular forms and to establish their associated properties.
• Definition and analysis of nearly holomorphic modular forms of half-integral weight.
• Extension of Shimura lifts to the specified forms.
• Proof of Hecke equivariance for the new lifts.
• Derivation of new Selberg identities relevant to this context.
• Successfully extended Shimura lifts to nearly holomorphic modular forms.
• Established Hecke equivariance for these extensions.
• Discovered new Selberg identities related to the extended Shimura lifts.