## Analytic Arithmetic in Algebraic Number Fields |

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### Contents

Classical background | 1 |

2 Group theoretic intermission p | 10 |

S3 Weils group and nonabelian Lfunctions p | 19 |

Copyright | |

15 other sections not shown

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### Common terms and phrases

Acad Algebraic Analysis applications assume asymptotic Banach space BERARD biconvex boundary bounded Chap Chapter complex condition consider constant converges convex Corollary curvature defined definition denote Diff dimension Dirichlet Dvoretzky's theorem Edited eigenfunctions eigenvalue problem elliptic elliptic operators equivalent estimate finite dimensional follows formula function Gaussian geodesic Geom given gr(k heat equation heat kernel hence Hilbert space implies Index Theorem integral isoperimetric inequality Laplace operator Laplacian lemma Let M,g linear manifold M,g MARCEL BERGER martingale Math Mathematics measure space Methods metric norm notations obtain orthogonal orthonormal PIERRE H preprint Proc Proceedings proof of theorem properties Proposition prove relation Remark representation resp Riemannian manifold Riemannian metric satisfies Seminar sequence sigma-algebra spectral geometry spectre spectrum SQ(k stable type stochastic subset subspace Suppose symmetric theory topology uniformly valeurs propres variables vector