Graphes de Ramanujan et applications
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...
Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.
Growth of Selmer groups of Hilbert modular forms over ring class fields
We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first a suitable parity result.
Grundlagen einer independenten Theorie der elliptischen Modulfunctionen und Theorie der Multiplicatorgleichungen erster Stufe.