Hilbert Modular Forms

Introduction Notations Moduli spaces of abelian varieties with real multiplication Properties of $\mathcal{G}$ Hilbert modular forms The $q$-expansion map The partial Hasse invariants Reduceness of the partial Hasse invariants A compactification of $\mathfrak{M} (k,\mu_{pN})^{\rm{Kum}}$ Congruences mod $p^n$ and Serre's $p$-adic modular forms Katz's $p$-adic Hilbert modular forms The operators $\Theta_{\mathfrak{P},i}$ The operator $V$ The operator $U$ Applications to filtrations of modular forms Theta cycles and parallel filtration (inert case) Functorialities Integrality and congruences for values of zeta functions Numerical examples Comments regarding values of zeta functions References