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The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.
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The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the liter
The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representa
This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interes
This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent pro
