Number Theory, Analysis and Geometry de Dorian Goldfeld

Number Theory, Analysis and Geometry: In Memory of Serge Lang

Dorian Goldfeld

Jay Jorgenson

Peter Jones

Dinakar Ramakrishnan

Kenneth Ribet

John Tate

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 of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life.This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.

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Cuprins

-Preface.-Introduction (Tate).-Publications by Serge Lang.-Raynaud's Group-Scheme and Reduction of Converings (Abramovich).-The Modular Degree, Congruence Primes, and Multiplicity One (Agashe, Ribet, Stein).-Le théorème de Siegel-Shidlovsky revisté (Bertrand).-Some Aspects of Harmonic Analysis on So3(Z[i])\So3(C)/SO(3), and SO(2,1)z\SO(2,1)/SO(2) (Brenner, Sinton).-Differential Characters on Curves (Buium).-Weyl Group Multpile Dirichlet Series of Type A_2 (Chinta, Gunnels).-Remarks on the Geometry of the Diffeomorphism Group of the Circle (Constantin, Kolev).-Harmonic Representatives For Cuspidal Cohomology Classes (Dodziuk, McGowan, Perry).-About the ABC Conjecture and an Alternative (van Frenkenhuijsen).-Unifying Themes Suggested by Belyi's Theorem (Goldring).-On the Local Divisibility of Heegner Points (Gross, Parson).-Uniform Estimates for Primitive Divisors in Elliptic Divisibility Sequences (Ingram, Silverman).-The Heat Kernel, Theta Inversion and Zetas on Gamma\G/K (Jorgenson, Lang).-Applications of Heat Kernels on Abelian Groups: zeta(2n), Quadratic Reciprocity, Bessel Integrals (Karlsson).-Report on the Irreducibility of L-Functions (Katz).-Remark on Fundamental Groups and Effective Diophantine Methods for Hyperbolic Curves (Kim).-Ranks of Elliptic Curves in Cubic Extensions (Kisilevsky).-On Effective Equidistribution of Expanding Tranlates of Certain Orbits in the Space of Lattices (Kleinbock, Margulis).-Elliptic Eisenstein Series for PSL2(Z) (Kramer, Pippich).-Consequences of the Gross-Zagier Formulae: Stability of Average L-Values, Subconvexity, and Non-Vanishing Mod p (Michel, Ramakrishnan).- A Variant of the Lang-Trotter Conjecture (Murty, Murty).-Multiplicity Estimates, Interpolation, and Transcendence Theory (Nakamaye).-Sampling Spaces and Arithmetic Dimension (O'Neil).-On the Birational Anabelian Program Initiated by Bogomolov (Pop).-Irreducible Spaces of Modular Units (Rohrlich).-Equidistribution and Generalized Mahler Measures (Szpiro, Tucker).-Représentations p-adiques de torsion admissibles (Vignéras).-Multiplier Ideal Sheaves, Nevanlinna Theory, and Diophantine Approximation (Vojta).-Report on Some Recent Advances in Diophantine Approximation (Waldschmidt).

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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

Number Theory, Analysis and Geometry: In Memory of Serge Lang

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