Hecke operators on period functions for Γ0(n)\Gamma_0(n)

Matrix representations of Hecke operators on classical holomorphical cusp forms and the corresponding period polynomials are well known. In this article we derive representations of Hecke operators for vector valued period functions for the congruence subgroups $\Gamma_0(n)$. For this we use an integral transform from the space of vector valued cusp forms to the space of vector valued period functions.Comment: v2: corrected version, submitted to Journal of Number, 29 pages, 1 figur

Eigenfunctions of transfer operators and cohomology

The eigenfunctions with eigenvalues 1 or -1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with coefficients in certain principal series representations

A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.Comment: 30 pages; corrected typos and fixed incomplete proofs in section

Calcium scoring using 64-slice MDCT, dual source CT and EBT: a comparative phantom study

Purpose Assessment of calcium scoring (Ca-scoring) on a 64-slice multi-detector computed tomography (MDCT) scanner, a dual-source computed tomography (DSCT) scanner and an electron beam tomography (EBT) scanner with a moving cardiac phantom as a function of heart rate, slice thickness and calcium density. Methods and materials Three artificial arteries with inserted calcifications of different sizes and densities were scanned at rest (0 beats per minute) and at 50–110 beats per minute (bpm) with an interval of 10 bpm using 64-slice MDCT, DSCT and EBT. Images were reconstructed with a slice thickness of 0.6 and 3.0 mm. Agatston score, volume score and equivalent mass score were determined for each artery. A cardiac motion susceptibility (CMS) index was introduced to assess the susceptibility of Ca-scoring to heart rate. In addition, a difference (Δ) index was introduced to assess the difference of absolute Ca-scoring on MDCT and DSCT with EBT. Results Ca-score is relatively constant up to 60 bpm and starts to decrease or increase above 70 bpm, depending on scoring method, calcification density and slice thickness. EBT showed the least susceptibility to cardiac motion with the smallest average CMS-index (2.5). The average CMS-index of 64-slice MDCT (9.0) is approximately 2.5 times the average CMS-index of DSCT (3.6). The use of a smaller slice thickness decreases the CMS-index for both CT-modalities. The Δ-index for DSCT at 0.6 mm (53.2) is approximately 30% lower than the Δ-index for 64-slice MDCT at 0.6 mm (72.0). The Δ-indexes at 3.0 mm are approximately equal for both modalities (96.9 and 102.0 for 64-slice MDCT and DSCT respectively). Conclusion Ca-scoring is influenced by heart rate, slice thickness and modality used. Ca-scoring on DSCT is approximately 50% less susceptible to cardiac motion as 64-slice MDCT. DSCT offers a better approximation of absolute calcium score on EBT than 64-slice MDCT when using a smaller slice thickness. A smaller slice thickness reduces the susceptibility to cardiac motion and reduces the difference between CT-data and EBT-data. The best approximation of EBT on CT is found for DSCT with a slice thickness of 0.6 mm

Coronary revascularization treatment based on dual-source computed tomography

Therapy advice based on dual-source computed tomography (DSCT) in comparison with coronary angiography (CAG) was investigated and the results evaluated after 1-year follow-up. Thirty-three consecutive patients (mean age 61.9 years) underwent DSCT and CAG and were evaluated independently. In an expert reading (the “gold standard”), CAG and DSCT examinations were evaluated simultaneously by an experienced radiologist and cardiologist. Based on the presence of significant stenosis and current guidelines, therapy advice was given by all readers blinded from the results of other readings and clinical information. Patients were treated based on a multidisciplinary team evaluation including all clinical information. In comparison with the gold standard, CAG had a higher specificity (91%) and positive predictive value (PPV) (95%) compared with DSCT (82% and 91%, respectively). DSCT had a higher sensitivity (96%) and negative predictive value (NPV) (89%) compared with CAG (91% and 83%, respectively). The DSCT-based therapy advice did not lead to any patient being denied the revascularization they needed according to the multidisciplinary team evaluation. During follow-up, two patients needed additional revascularization. The high NPV for DSCT for revascularization assessment indicates that DSCT could be safely used to select patients benefiting from medical therapy only