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We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncom-pact finite volume Riemann surface S under deformation of the surface. Our calculations indicate that if the Teichmüller space of S is not trivial, then each cusp form has a set of deformations under which either the cusp… (More)
Let T N,χ p,k (x) be the characteristic polynomial of the Hecke operator T p acting on the space of cusp forms S k (N, χ). We describe the factorization of T N,χ p,k (x) mod ℓ as k varies, and we explicitly calculate those factorizations for N = 1 and small ℓ. These factorizations are used to deduce the irreducibility of certain T 1,1 q,k (x) from the… (More)
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U (N), O(2N) and U Sp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum,… (More)
CT scans were obtained with a Cine-CT Scanner that uses a rapidly moving focused electron beam. The 50-msec CT scans were obtained at two transverse levels simultaneously through the hearts of a series of four normal dogs and six patients, four with coronary artery disease and two with hypertrophic cardiomyopathy. Two scanning mode options were chosen.… (More)
A prototype ultrafast cine computed tomographic (CT) scanner, designed specifically for cardiac imaging, was used to evaluate a preliminary series of patients with prior myocardial infarction (n = 21) and a control group without coronary artery disease (n = 5). Multilevel 50-msec CT scan exposures were obtained during peripheral intravenous bolus injections… (More)
BACKGROUND/AIMS Hepatitis C (HCV) infected patients have significant health-related quality of life (HRQL) impairment which worsens during anti-viral therapy. Our aim was to examine the association of HRQL with treatment-induced depression and anemia. METHODS Two hundred and seventy-one HCV patients who received pegylated interferon alfa 2b and ribavirin… (More)
Magnetic resonance imaging (MRI) was conducted with use of the spin-echo technique (0.35 Tesla) in 22 patients with a variety of congenital and cardiovascular anomalies and in 16 normal volunteers. Electrocardiographic (ECG) synchronization of the data acquisition produced transverse, parasagittal, and coronal tomograms that were used to define size and… (More)
Let T p,k (x) be the characteristic polynomial of the Hecke operator Tp acting on the space of level 1 cusp forms S k (1). We show that T p,k (x) is irreducible and has full Galois group over Q for k ≤ 2000 and p < 2000, p prime.
For each prime p, we determine the distribution of the p th Fourier coefficients of the Hecke eigenforms of large weight for the full modular group. As p → ∞, this distribution tends to the Sato–Tate distribution.