On primitive lattice points in planar domains
On primitive roots.
On products and interminate powers of sequences
On products of eigenforms
On products of singular elements
On products of special linear forms with algebraic coefficients
On prolongations of rank one discrete valuations
Let be a valued field, where is a rank one discrete valuation. Let be its ring of valuation, its maximal ideal, and an extension of , defined by a monic irreducible polynomial . Assume that factors as a product of distinct powers of monic irreducible polynomials. In this paper a condition which guarantees the existence of exactly distinct valuations of extending is given, in such a way that it generalizes the results given in the paper “Prolongations of valuations to finite...
On properties of systems of arithmetic sequences
On pseudoprime numbers of special form
On pseudoprimes having special forms and a solution of K. Szymiczek’s problem
We use the properties of -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
On pseudorandom binary lattices
On Pyramidal Numbers of Order 4.
On pythagorean angles
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.