Includes bibliographical references.

Mesure de Mahler et regulateur elliptique: Preuve de deux relations exotiques ; The adic height pairings of Coleman-Gross and of Nekovar ; Dirichlet series for squares of sums of squares: A summary ; Equivariant Whitehead torsion and refined Euler characteristics ; Questions about the reductions modulo primes of an elliptic curve ; New perspectives in Arakelov geometry ; A fourteenth lecture on Fermat's last theorem ; Number fields with large class group ; Period polynomials for mathbb F_q of fixed small degree ; Some recent results about (ternary) quadratic forms ; An extension of a theorem of D. H. Lehmer ; On a family of real bicyclic biquadratic fields ; Belyi parametrisations of elliptic curves and congruence defects ; An application of exterior square functoriality of L_4 ; Asai lift ; Totally real integral points on a plane algebraic curve ; On the largest prime factor of a Mersenne number ; On the adic series sum _n=1^\infty n^k\cdot n! ; Hecke operators and the expansion of modular forms ; An ABC construction of number fields ; Diophantine approximation in small degree ; Compact operators with rational generation ; The canonical height of a finite etale algebra