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Subconvexity of L-functions - Part 1 - Michel, Philippe (Author of the conference) | CIRM H

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]
The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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Subconvexity of L-functions - Part 2 - Michel, Philippe (Author of the conference) | CIRM H

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]
The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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Subconvexity of L-functions - Part 3 - Nelson, Paul (Author of the conference) | CIRM H

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]
The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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Subconvexity of L-functions - Part 4 - Nelson, Paul (Author of the conference) | CIRM H

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]
The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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This is a work with Yves Colin de Verdière, Charlotte Dietze and Maarten De Hoop, motivated by recent works by M. De Hoop on inverse problems for sound wave propagation in gas giant planets. On such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with a boundary whose metric blows up near the boundary. With appropriate variable changes, we can reduce the study of the Laplacian?Beltrami to that of a kind of sub-Riemannian Laplacian. In this talk, I will explain how to approach the spectral analysis of such operators, and in particular how to calculate WeylÕs law.[-]
This is a work with Yves Colin de Verdière, Charlotte Dietze and Maarten De Hoop, motivated by recent works by M. De Hoop on inverse problems for sound wave propagation in gas giant planets. On such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with a boundary whose metric blows up near the boundary. With appropriate variable changes, we can reduce the study of ...[+]

11F72 ; 58C40 ; 53C22 ; 37D40 ; 53C65 ; 35R30

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In joint work with Luc Hillairet, we show that the Laplacian associated with the generic finite area triangle in hyperbolic plane with one vertex of angle zero has no positive Neumann eigenvalues. This is the first evidence for the Phillips-Sarnak philosophy that does not depend on a multiplicity hypothesis. The proof is based an a method that we call asymptotic separation of variables.

58J50 ; 35P05 ; 11F72

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Lecture 1: Distinction and the geometric lemma - Offen, Omer (Author of the conference) | CIRM H

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Lecture 2: Distinction by a symmetric subgroup - Offen, Omer (Author of the conference) | CIRM H

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Lecture 4: The relative trace formula - Offen, Omer (Author of the conference) | CIRM H

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