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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]

The goal of this paper was to explain certain experimentally observed properties of the (cuspidal) spectrum and its associated automorphic forms (Maass waveforms) on the congruence subgroup Γ0(9). The first property is that the spectrum possesses multiplicities in the so-called new part, where it was previously believed to be simple. The second property is that the spectrum does not contain any ‘genuinely new’ eigenvalues, in the sense that all eigenvalues of Γ0(9) appear in the spectrum of some congruence subgroup of lower level.The main theorem in this paper gives a precise decomposition of the spectrum of Γ0(9) and in particular, we show that the genuinely new part is empty. We also prove that there exist an infinite number of eigenvalues of Γ0(9) where the corresponding eigenspace is of dimension at least two and has a basis of pairs of Hecke-Maass newforms which are related to each other by a character twist. These forms are non-holomorphic analogues of modular forms with inner twists and also provide explicit (affirmative) examples of a conjecture stating that if the Hecke eigenvalues of two ‘generic’ Maass newforms coincide on a set of primes of density ½ then they have to be related by a character twist. [ABSTRACT FROM PUBLISHER]

Objective. To evaluate the reliability of cause-of-death diagnoses among prostate cancer patients. Material and methods. Information from death certificates obtained from the Swedish Death Register was compared with systematically reviewed medical records from the population-based Swedish Regional Prostate Cancer Register, South-East Region. In total, 5675 patients were included who had been diagnosed with prostate cancer between 1987 and 1999 and who had died before 1 January 2003. Results. The proportion of prostate cancer cases classified as having died from prostate cancer was 3% higher in the official death certificates than in the reviewed records [0.03, 95% confidence interval (CI) 0.02 to 0.04]. Overall agreement between the official cause of death and the reviewed data was 86% (95% CI 85 to 87%). A higher accuracy was observed among men with localized disease (88%, 95% CI 87 to 89%), aged 60 years or younger at death (96%, 95% CI 93 to 100%), or who had undergone curative treatment (91%, 95% CI 88 to 95%). This study indicates a relatively high reliability of official cause-of-death statistics of prostate cancer patients in Sweden. Conclusion. Mortality data obtained from death certificates may be useful in the evaluation of large-scale prostate cancer intervention programmes, especially among younger patients with localized disease. [ABSTRACT FROM AUTHOR]

We construct Hecke operators acting on Maass waveforms of integer non-zero weight and transforming according to a non-trivial multiplier system on the modular group. Using these Hecke operators we obtain multiplicativity relations for the Fourier coefficients of such Maass waveforms. These relations generalize the usual weight zero relations. We also obtain an unexpected relation between coefficients with positive and negative indices with a constant of proportionality involving the Laplace eigenvalue (see Theorem 3.1 (2)–(4) and §5). Numerical examples of multiplicativity relations are given at the end of the paper. [ABSTRACT FROM PUBLISHER]

The Rankin convolution type Dirichlet series DF,G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series DF,G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail. [ABSTRACT FROM AUTHOR]

Objective. To analyse the management of muscle-invasive bladder cancer in a population-based national register, and specifically to investigate the role of curative therapy (i.e. cystectomy or radiotherapy) in relation to patient, tumour and hospital characteristics. Material and methods. The Swedish Bladder Cancer Register covers more than 90% of all patients in the country who have been diagnosed with such disease since 1997. Results from 1997-2003 were analysed regarding curative-intent treatment given within 3-6 months of diagnosis of muscle-invasive bladder cancer. Results. In total, 3463 patients with clinical T2-T4 bladder cancer were included in the analysis. Of those patients, 1426 (41%) received curative-intent treatment in the form of radiotherapy (285, 20%) or cystectomy (1141, 80%). Male gender, age < 76 years, favourable TNM category and registration at a high-volume hospital were associated with such treatment. Curative-intent treatment was given to significantly more patients registered at high-volume hospitals (1003/2227, 45%) than at low-volume hospitals (423/1235, 34%) (χ2=37.7, p<0.00001). Cystectomy was performed more often in those registered at high-volume than at low-volume hospitals (826/2227, 37%, and 316/1235, 26%, respectively, χ2=47.3, p<0.00001). Conclusions. Lower rates of curative-intent treatment were found in patients registered at low-volume than at high-volume facilities, and the same was seen when comparing females with males, and patients aged 76-80 years with younger patients. Since many of these bladder cancer patients were registered at and eventually treated at hospitals handling fewer than 10 such cases annually, it seems desirable to concentrate treatment of this disease at more specialized centres. [ABSTRACT FROM AUTHOR]