1,082 research outputs found

    Character sums for primitive root densities

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    It follows from the work of Artin and Hooley that, under assumption of the generalized Riemann hypothesis, the density of the set of primes qq for which a given non-zero rational number rr is a primitive root modulo qq can be written as an infinite product pδp\prod_p \delta_p of local factors δp\delta_p reflecting the degree of the splitting field of XprX^p-r at the primes pp, multiplied by a somewhat complicated factor that corrects for the `entanglement' of these splitting fields. We show how the correction factors arising in Artin's original primitive root problem and some of its generalizations can be interpreted as character sums describing the nature of the entanglement. The resulting description in terms of local contributions is so transparent that it greatly facilitates explicit computations, and naturally leads to non-vanishing criteria for the correction factors. The method not only applies in the setting of Galois representations of the multiplicative group underlying Artin's conjecture, but also in the GL2_2-setting arising for elliptic curves. As an application, we compute the density of the set of primes of cyclic reduction for Serre curves.Comment: 23 pages. This version is to appear in the Mathematical Proceedings of the Cambridge Philosophical Societ

    For the time being

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    This paper is a reflection on my journey away from painting and my recent effort to broaden my understanding of internal and external experience by exploring language and the material world. This journey has led me a few steps closer to finding my voice as an artist. It loosed the threads of thought, multiple and variable, that comprise this thesis body of work

    Effects of interleukin-3 on myelosuppression induced by chemotherapy for ovarian cancer and small cell undifferentiated tumours.

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    Two clinical studies were undertaken to study the toxicity profile and effects of interleukin-3 (rhIL-3) on chemotherapy-induced myelosuppression. Fifteen patients with recurrent ovarian carcinoma were treated with high dose carboplatin (800 mg m-2). All patients received 5.0 micrograms/kg/d rhIL-3 subcutaneously but timing and duration of rhIL-3 treatment differed. Constitutional symptoms were the major toxicity and in addition to the carboplatin-induced nausea and vomiting the combination was poorly tolerated. In 5/15 patients receiving high dose carboplatin rhIL-3 administration was discontinued due to nephrotoxicity (2 x), hypotension, severe malaise and bone pain. In this study, rhIL-3 ameliorated chemotherapy-induced neutropenia as well as thrombocytopenia and reduced the requirement for platelet transfusions in the second cycle of chemotherapy. However, rhIL-3 failed to prevent cumulative platelet toxicity. In the second study 12 patients with small cell undifferentiated cancers were treated with carboplatin, etoposide and ifosfamide. Three dose levels of rhIL-3 were explored (0.125, 5.0 and 7.5 micrograms/kg/d). In this study, toxicity of the treatment was mild, however, no beneficial haematologic effects of rhIL-3 could be demonstrated. In conclusion, the haematological effects of rhIL-3 were modest and dependent on the chemotherapeutic regimen, timing and duration of rhIL-3 treatment (in relation to the expected nadir). In general rhIL-3-induced toxicity was mild, but combination with high dose carboplatin could be hazardous if rhIL-3 is initiated at 24 h after the cytostatic agent

    Prognostic factors in high and intermediate grade non-Hodgkin's lymphoma.

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    An analysis of prognostic factors has been performed on 260 patients with high and intermediate grade non-Hodgkin's lymphoma (NHL) treated over an 11-year period between 1975 and 1986. The overall 5-year survival rate was 50% with a median follow-up of 72 months. Over 20 clinical, radiological and laboratory parameters have been studied, including variables reported to be important indicators of prognosis in previous series, and these variables have been subjected to univariate and multivariate analysis. Attainment of complete remission (CR) was the most important predictor of overall survival, low serum lactate dehydrogenase (LDH), limited stage disease and a high serum albumin were also independently associated with prolonged survival in multivariate analysis. After removing remission status from the model, Ann Arbor clinical stage became the most significant pre-treatment prognostic indicator. Sixty-five per cent of patients achieved CR, and a discriminant analysis showed that failure to attain CR was associated with advanced stage disease, constitutional symptoms, increasing patient age, a low serum albumin and the presence of bulk disease. Advanced clinical stage and an elevated serum LDH predicted independently for a poor relapse-free survival, and reduced overall survival following CR. There was no significant correlation between histological subtype in the Kiel classification and prognosis. This study confirms the prognostic significance of remission status and Ann Arbor clinical stage, and illustrates additional factors including serum levels of albumin and LDH, which serve to enhance the pre-treatment prognostic evaluation of patients with unfavourable histology NHL

    A pilot study to evaluate the effects of C1 esterase inhibitor on the toxicity of high-dose interleukin 2.

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    In a pilot study six patients received 4 days' treatment with interleukin 2 (IL-2) [cumulative dose (CD) 264 +/- 26 x 10(6) IU m-2] and C1 esterase inhibitor (C1-INH) (loading dose 2,000 U, followed by 500-1,000 U twice daily). Toxicity was compared with that in patients given 4 days' treatment with standard (CD 66 +/- 12 x 10(6) IU m-2) or escalating-dose (CD 99 +/- 8 x 10(6) IU m-2) IL-2. IL-2-induced hypotension was equivalent and complement activation was less after IL-2 + C1-INH (C3a = 10.5 +/- 3.2 nmol l-1) than following standard (14.1 +/- 8.4 nmol l-1) or escalating-dose (18.3 +/- 2.9 nmol l-1) IL-2. This study demonstrates that C1-INH administration during IL-2 treatment is safe and warrants further study to evaluate its ability to ameliorate IL-2-induced toxicity
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