Special Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular Forms

Raveena Ganash

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arXiv · 2608.12542

Special Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular Forms

Raveena Ganash

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Abstract

We find the adjoint of a map on the space of almost holomorphic modular forms, analogous to the generalized Ramanujan-Serre derivative on the space of quasi-modular forms. As applications, we explicitly find special values of certain shifted Dirichlet series associated to quasi-modular forms and prove a rationality result for the shifted Dirichlet series.

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Raveena Ganash. 2026-08-12. Special Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular Forms. https://arxiv.org/abs/2608.12542

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