Number theory, analysis and geometry [electronic resource] : in memory of Serge Lang / Dorian Goldfeld [and others], editors.
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, ¡and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subjec...
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| 505 | 0 | |a Number Theory, Analysis and Geometry; Preface; Contents; Publications of Serge Lang: from 2000 and beyond; Introduction; Raynaud's group-scheme and reduction of coverings; 1 Introduction; 1.1 Reduction of coverings of degree divisible by p; 1.2 Background; 1.3 Towards a proper moduli space; 1.4 Brief introduction to twisted curves; 1.5 Acknowledgements; 2 Extensions of group-schemes and their actionsin dimension 1 and 2; 2.1 Raynaud's group-scheme; 2.2 Extension from codimension 1 to codimension 2; 3 Curves; 3.1 The smooth locus; 3.2 The structure of Y and G over nodes and markings of X. | |
| 505 | 8 | |a A.1 Some algebraA. 2 Endomorphisms of the fundamental formal group; References; The modular degree, congruence primes, and multiplicity one; 1 Introduction; 2 Elliptic curves; 2.1 Modular degree and congruence number; 2.2 Multiplicity one and its failure; 3 Modular abelian varieties of arbitrary dimension; 4 Proof of Theorem 3.6(a); 5 Proof of Theorem 3.6(b); 5.1 The congruence and intersection ideals; 5.2 Multiplicity one for differentials; 5.2.1 Failure of multiplicity one for differentials; 5.2.2 Proof of Proposition 5.10; 6 Duality theory: an appendix by Brian Conrad; References. | |
| 505 | 8 | |a Le théorème de Siegel-Shidlovsky revisité1 Introduction; 2 Le lemme de zéros; 3 Les deux premières étapes, et le lemme d'interpolation de M. Laurent; 4 Conclusion de la première preuve (cas général); 5 Conclusion de la seconde preuve (cas de Lindemann-Weierstrass); 6 L'approche duale; References; Some aspects of harmonic analysis on locally symmetric spaces related to real-form embeddings; 1 Obtaining the heat kernel by integration over a normal bundle; 1.1 Setup and notation; 1.2 Integral formulas; 1.3 Differential operators and the heat kernels; 2 Fundamental Domains. | |
| 505 | 8 | |a 2.1 Representation of SO3(Z[i]) as a lattice in SL2(C)2.2 Good Grenier fundamental domains for arithmetic groups Aut+(H3); 2.3 Explicit description of the fundamental domain for the action of SO3(Z[i]) on H3; 2.4 SO(2,1)Z as a group of fractional linear transformations; 2.5 Fundamental domain for SO(2,1)Z acting on H2 and its relation to that of SO3(Z[i]); 2.6 Spectral zeta functions; References; Differential characters on curves; 1 Introduction; 2 Main concepts and statement of the theorem; 3 Proof of the theorem; References; Weyl group multiple Dirichlet series of type A2; 1 Introduction. | |
| 505 | 8 | |a 2 A Weyl group action3 Kubota's Dirichlet series; 4 The double dirichlet series; References; On the geometry of the diffeomorphism group of the circle; 1 Introduction; 2 Invariant metrics on an abstract Lie group; 2.1 Left-invariant metrics; 2.2 Angular velocities and momenta; 2.3 Noether's theorem; 2.4 Euler's equations; 2.5 The contravariant formulation; 2.6 Right-invariant metrics; 3 Right-invariant metrics on the diffeomorphism group of the circle; 3.1 Right-invariant metrics on Diff(S1); 3.2 Examples; 3.3 Regular dual; 3.4 The momentum; 3.5 The Cauchy problem; 3.6 The exponential map. | |
| 520 | |a Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, ¡and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas, namely number theory, analysis and geometry, representing Lang's own breadth of interests.¡A special introduction by John Tate includes a brief and engaging account of Serge Lang's life. Contributors to the volume: D. Abramovich A. Agashe D. Bertrand E. Brenner A. Buium G. Chinta A. Constantin J. Dodziuk M. van Frankenhuijsen W. Goldring B.H. Gross P.E. Gunnells P. Ingram J. Jorgenson A. Karlsson N.M. Katz M. Kim H. Kisilevsky D.Y. Kleinbock B. Kolev J. Kramer S. Lang J. Lubin G.A. Margulis J. McGowan P. Michel M.R. Murty V.K. Murty M. Nakamaye C. O'Neil J.A. Parson P. Perry A.-M. von Pippich F. Pop D. Ramakrishnan K.A. ¡Ribet D.E. Rohrlich J.H. Silverman A. Sinton W.A. Stein L. Szpiro J. Tate T.J. Tucker M.-F. Vignéras P. Vojta M. Waldschmidt. | ||
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