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A hyperelliptic curve over $\mathbb Q$ is called "locally soluble" if it has a point over every completion of $\mathbb Q$. In this paper, we prove that a positive proportion of hyperelliptic curves over $\mathbb Q$ of genus $g\geq 1$ are... more
A hyperelliptic curve over $\mathbb Q$ is called "locally soluble" if it has a point over every completion of $\mathbb Q$. In this paper, we prove that a positive proportion of hyperelliptic curves over $\mathbb Q$ of genus $g\geq 1$ are locally soluble but have no points over any odd degree extension of $\mathbb Q$. We also obtain a number of related results. For example, we prove that for any fixed odd integer $k > 0$, the proportion of locally soluble hyperelliptic curves over $\mathbb Q$ of genus $g$ having no points over any odd degree extension of $\mathbb Q$ of degree at most $k$ tends to 1 as $g$ tends to infinity. We also show that the failures of the Hasse principle in these cases are explained by the Brauer-Manin obstruction. Our methods involve a detailed study of the geometry of pencils of quadrics over a general field of characteristic not equal to 2, together with suitable arguments from the geometry of numbers.
We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes... more
We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel and Fourier-Jacobi models too. We formulate several conjectures about these restriction problems involving root numbers of symplectic representations in the local case, and central critical L-value in the global case. Along the way we prove several results both in number theory and representation theory.
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... Noam D. Elkies and Benedict H. Gross Contents 1. The exceptional cone in R27 .....666 2. Choosing a polarization.....669 3. Jordan roots ..... ...
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We develop a theory of Fourier coefficients for modular forms on the split exceptional group G<sub>2</sub> over ℚ.
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The method of Chabauty can then be used to obtain an effective bound on the number of rational points on most of these hyperelliptic curves; for example, we show that a majority of hyperelliptic curves of genus $n\geq 3$ with a rational... more
The method of Chabauty can then be used to obtain an effective bound on the number of rational points on most of these hyperelliptic curves; for example, we show that a majority of hyperelliptic curves of genus $n\geq 3$ with a rational Weierstrass point have fewer than 20 rational points.
In an earlier paper, we considered several restriction problems in the representation theory of classical groups over local and global fields. Assuming the Langlands-Vogan parameterization of irreducible representations, we formulated... more
In an earlier paper, we considered several restriction problems in the representation theory of classical groups over local and global fields. Assuming the Langlands-Vogan parameterization of irreducible representations, we formulated precise conjectures for the solutions of these restriction problems. In the local case, our conjectural answer is given in terms of Langlands parameters and certain natural symplectic root numbers associated
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Preoperative CT scans of 33 patients with esophageal cancer were reviewed to assess staging accuracy and define the role of CT in patients being considered for transhiatal blunt esophagectomy. Surgical and pathological verification was... more
Preoperative CT scans of 33 patients with esophageal cancer were reviewed to assess staging accuracy and define the role of CT in patients being considered for transhiatal blunt esophagectomy. Surgical and pathological verification was obtained in all cases. Only 13 tumors were staged correctly according to the TNM classification. In addition, CT was not useful in assessing resectability because of its low accuracy in evaluating aortic invasion and the fact that few patients had tracheobronchial or aortic invasion or hepatic metastases at presentation.
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Two methods for the measurement of the electron emission currents and the secondary electron yields for electron-irradiated dielectrics are discussed. Experimental results indicate that the dynamic measurement method for the secondary... more
Two methods for the measurement of the electron emission currents and the secondary electron yields for electron-irradiated dielectrics are discussed. Experimental results indicate that the dynamic measurement method for the secondary emission yield δ provides yield curves that are significantly lower than those obtained by conventional methods, at least in the region in which δ goes through a maximum. This
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Page 1. MATHEMATICS OF COMPUTATION Volume 74, Number 251, Pages 1545–1557 S 0025-5718(04)01709-0 Article electronically published on September 10, 2004 COMPUTING WEIGHT 2 MODULAR FORMS OF LEVEL p2 ...
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Abstract In a previous paper [EG] we described an integral structure (J, E) on the exceptional Jordan algebra of Hermitian 3× 3 matrices over the Cayley octonions. Here we use modular forms and Niemeier's classification of even... more
Abstract In a previous paper [EG] we described an integral structure (J, E) on the exceptional Jordan algebra of Hermitian 3× 3 matrices over the Cayley octonions. Here we use modular forms and Niemeier's classification of even unimodular lattices of rank 24 to further ...
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We develop a theory of Fourier coefficients for modular forms on the split exceptional group G<sub>2</sub> over ℚ.
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Computed tomography (CT) has been used to detect a variety of gallbladder abnormalities, but the accuracy of routine abdominal CT in evaluating intracholecystic bile has not been established. Forty-six patients were identified in whom... more
Computed tomography (CT) has been used to detect a variety of gallbladder abnormalities, but the accuracy of routine abdominal CT in evaluating intracholecystic bile has not been established. Forty-six patients were identified in whom abdominal CT and sonography were performed within 1 week of each other. Using sonographic results as the standard, sensitivity, specificity, and accuracy of CT gallbladder evaluation were calculated; both initial CT interpretations and retrospective review of scans were used for this analysis. In the retrospective review, visual interpretation of gallbladder images and measurement of intracholecystic bile attenuation (greater than or equal to 25 H, abnormal) were analyzed. The overall sensitivity of CT in detecting abnormal gallbladder contents ranged from 44% (bile attenuation greater than or equal to 25 H) to 63% (retrospective CT interpretation), while specificity ranged from 77% to 93%. The most common cause of high-attenuation bile in the series was sludge, a cause not previously reported. It was concluded that intracholecystic bile is poorly evaluated on routine abdominal CT, particularly because of low sensitivity in disease detection.
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CT was used to investigate the number and size of normal mediastinal lymph nodes at 11 intrathoracic nodal stations defined by the American Thoracic Society lymph-node mapping scheme. Nodal size was measured both as short- and long-axis... more
CT was used to investigate the number and size of normal mediastinal lymph nodes at 11 intrathoracic nodal stations defined by the American Thoracic Society lymph-node mapping scheme. Nodal size was measured both as short- and long-axis diameters in the transverse plane. Findings for 56 patients show the largest normal mediastinal nodes to be in the subcarinal and right tracheobronchial regions. Upper paratracheal nodes were smaller than lower paratracheal or tracheobronchial nodes, and right-sided tracheobronchial nodes were larger than left-sided ones. From the distributions of node sizes, thresholds were set above which nodes in any region might be considered enlarged. These thresholds, in agreement with a prior investigation of patients with lung cancer, suggest 1.0 cm as the upper limit of normal for the short axis of a mediastinal node in the transverse plane.