Generalized Eisenstein series and modified Dedekind sums.
Generalized Eta-Functions and Certain Ray Class Invariants of Real Quadratic Fields.
Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields
We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.
Generators and defining equation of the modular function field of the group Γ₁(N)
Generators and equations for modular function fields of principal congruence subgroups
Gravity, strings, modular and quasimodular forms
Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...
Grundlagen einer independenten Theorie der elliptischen Modulfunctionen und Theorie der Multiplicatorgleichungen erster Stufe.