On -Euler numbers related to the modified -Bernstein polynomials.
On q-Euler numbers, q-Salié numbers and q-Carlitz numbers
On q-orders in primitive modular groups
We prove an upper bound for the number of primes p ≤ x in an arithmetic progression 1 (mod Q) that are exceptional in the sense that has no generator in the interval [1,B]. As a consequence we prove that if with a sufficiently large absolute constant c, then there exists a prime q dividing Q such that for some positive integer b ≤ B. Moreover we estimate the number of such q’s under suitable conditions.
On quadratic character twists of Hecke L-functions attached to cusp forms of varying weights at the central point
On quadratic forms.
On Quadratic Forms in 3-Manifolds.
On Quadratic forms isotropic over the function field of a comic.
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...