Search

We give an explicit construction of lifting maps from integral and half-integral modular forms to vector-valued modular forms for Weil representations associated with arbitrary isotropic subgroups and finite quadratic modules of even and odd signature. This construction provides an explicit and general extension of previous work by Scheithauer and Zhang. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [20]. The exposition is self-contained and sufficient details are given for the reader to understand how it works and implement their own version if desired. [ABSTRACT FROM AUTHOR]

Abstract The main topic of the paper is spectral theory for noncongruence subgroups of the modular group. We have studied a selection of the main conjectures in the area: the Roelcke–Selberg and Phillips–Sarnak conjectures and Selberg's conjecture on exceptional eigenvalues. The first two concern the existence and nonexistence of an infinite discrete spectrum for certain types of Fuchsian groups and last states that there are no exceptional eigenvalues for congruence subgroups, or in other words, there is a specific spectral gap in the cuspidal spectrum. Our main theoretical result states that if the corresponding surface has a reflectional symmetry which preserves the cusps then the Laplacian on this surface has an infinite number of "new" discrete eigenvalues. We define old and new spaces of Maass cusp forms for noncongruence subgroups in a way that provides a natural generalization of the usual definition from congruence subgroups and give a method for determining the structure of the old space algorithmically. In addition to the theoretical result we also present computational data, including a table of subgroups of the modular group and eigenvalues of Maass forms for noncongruence subgroups. We also present, for the first time, numerical examples of both exceptional and (non-trivial) residual eigenvalues. To be able to (even heuristically) certify lists of computed eigenvalues we also proved an explicit average Weyl's law in this setting. [ABSTRACT FROM AUTHOR]

The last few years have seen a flurry of academic activities on comics in the Nordic countries. But are we on the verge of establishing an independent field or a discipline of comics studies, or both? And if so, is this desirable? On an international level, comics studies have for some time been an intellectual field and can now be said to be on a pre-paradigmatic level as a discipline. In the Nordic countries, the field of comics studies has grown rapidly the last few years, but it is still very much dispersed, with researchers working at different departments and within a number of disciplines. There are tendencies towards a maturing into a more cohesive field, but this is a recent development. The establishing of a comics studies discipline, though keeping an open ‘rural mode’ of knowledge production to prevent a loss of the positive aspects of interdisciplinary research, would facilitate the possibilities for professors’ seats, journals, specific grants, recurring conferences and research libraries – and thus a more rapid growth of comics studies. [ABSTRACT FROM PUBLISHER]