MODULAR AND AUTOMORPHIC FORMS & BEYOND

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Focusing on a new theory of modular forms, this monograph aims to integrate existing theories from various fields, including congruence groups and automorphic forms on Hermitian symmetric domains. It explores advanced concepts like Calabi-Yau modular forms and their applications, such as Yukawa couplings and topological string partition functions. A key element of this theory is the innovative use of the "Gauss-Manin connection in disguise," which serves as a foundational component to extend the current understanding of modular forms.