Number Theory, Analysis and Geometry

-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).