On quadratic forms of height 3 and degree . (Sur les formes quadratiques de hauteur 3 et de degré au plus 2.)
On quasi-periods of abelian functions with complex multiplication
On quotients of the space of orderings of the field ℚ(x)
In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings - it is, in general, nontrivial to determine whether, for a subgroup the derived quotient structure is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.
On R. Chapman's "evil determinant": case p ≡ 1 (mod 4)
For p ≡ 1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the (p+1)/2 × (p+1)/2 matrix with .
On rainbow arithmetic progressions.
On Ramanujan congruences between special values of Hecke and Dirichlet L-functions
On Ramanujan expansions of certain arithmetical functions
On Ramanujan's continued fraction
On Ramanujan's cubic continued fraction
On Ramanujan's formula for values of Riemann zeta-function at positive odd integers
On ramification and genus of recursive towers.
On Rank 4 Quadratic Spaces with Given Arf and Witt Invariants.
On ranks of Jacobian varieties in prime degree extensions
T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials...
On rapid generation of .
On ratio sets of natural numbers
On rational and integral roots of a polynomial
On rational approximations of algebraic numbers .
On rational approximations to Euler's constant and to .
On rational automorphs of quadratic forms
On rational Morley triangles