Primitive lattice points in convex planar domains
Primitive lattice points in planar domains
Primitive Lattice Points in Rational Ellipses and Relates Arithmetic Functions.
Primitive lattice points inside an ellipse
Let be a positive definite binary quadratic form with arbitrary real coefficients. For large real , one may ask for the number of primitive lattice points (integer points with ) in the ellipse disc , in particular, for the remainder term in the asymptotics for . While upper bounds for depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value or...
Primitive Lucas d-pseudoprimes and Carmichael-Lucas numbers
Let d be a fixed positive integer. A Lucas d-pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U(P,Q) such that the rank of appearance of N in U(P,Q) is exactly (N-ε(N))/d, where the signature ε(N) = (D/N) is given by the Jacobi symbol with respect to the discriminant D of U. A Lucas d-pseudoprime N is a primitive Lucas d-pseudoprime if (N-ε(N))/d is the maximal rank of N among Lucas sequences U(P,Q) that exhibit N as a Lucas pseudoprime. We derive...
Primitive minima of positive definite quadratic forms
The main purpose of the reduction theory is to construct a fundamental domain of the unimodular group acting discontinuously on the space of positive definite quadratic forms. This fundamental domain is for example used in the theory of automorphic forms for GLₙ (cf. [11]) or in the theory of Siegel modular forms (cf. [1], [4]). There are several ways of reduction, which are usually based on various minima of the quadratic form, e.g. the Korkin-Zolotarev method (cf. [10], [3]), Venkov's method...
Primitive newforms of weight 3/2
Primitive Points on a Modular Hyperbola
For positive integers m, U and V, we obtain an asymptotic formula for the number of integer points (u,v) ∈ [1,U] × [1,V] which belong to the modular hyperbola uv ≡ 1 (mod m) and also have gcd(u,v) =1, which are also known as primitive points. Such points have a nice geometric interpretation as points on the modular hyperbola which are "visible" from the origin.
Primitive points on elliptic curves
Primitive prime divisors in polynomial arithmetic dynamics.
Primitive prime factors in second-order linear recurrence sequences
Primitive quadratics reflected in -sequences.
Primitive representation of a binary quadratic form as a sum of four squares
Primitive roots and powers among values of polynomials over finite fields.
Primitive roots and quadratic non-residues
Primitive substitutive numbers are closed under rational multiplication
Let denote the set of real numbers whose base- digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the set is closed under multiplication by rational numbers, but not closed under addition.
Primitivmengen in additiven abelschen Gruppen.
Primteiler von Polynomen.
Primzahlen.
Primzahlen als achte Potenzreste.