Number Theory

Mesure de Mahler et regulateur elliptique: Preuve de deux relations exotiques by M. J. Bertin The $p$-adic height pairings of Coleman-Gross and of Nekovar by A. Besser Dirichlet series for squares of sums of squares: A summary by J. M. Borwein and K.-K. S. Choi Equivariant Whitehead torsion and refined Euler characteristics by D. Burns Questions about the reductions modulo primes of an elliptic curve by A. C. Cojocaru New perspectives in Arakelov geometry by C. Consani and M. Marcolli A fourteenth lecture on Fermat's last theorem by H. Darmon Number fields with large class group by W. Duke Period polynomials for $\mathbb{F}_q$ of fixed small degree by S. J. Gurak Some recent results about (ternary) quadratic forms by J. Hanke An extension of a theorem of D. H. Lehmer by L. Jones On a family of real bicyclic biquadratic fields by S.-i. Katayama, C. Levesque, and T. Nakahara Belyi parametrisations of elliptic curves and congruence defects by C. Khare An application of exterior square functoriality of $GL_4$; Asai lift by H. H. Kim Totally real integral points on a plane algebraic curve by M. Laurent On the largest prime factor of a Mersenne number by L. Murata and C. Pomerance On the $p$-adic series $\sum_{n=1}^{\infty} n^k\cdot n!$ by M. R. Murty and S. Sumner Hecke operators and the $q$-expansion of modular forms by K. Ono An ABC construction of number fields by D. P. Roberts Diophantine approximation in small degree by D. Roy Compact operators with rational generation by L. Smithline The canonical height of a finite etale $K$-algebra by V. Talamanca.