Rational sequences converging to .
Rational solutions of certain Diophantine equations involving norms
We present some results concerning the unirationality of the algebraic variety given by the equation , where k is a number field, K=k(α), α is a root of an irreducible polynomial h(x) = x³ + ax + b ∈ k[x] and f ∈ k[t]. We are mainly interested in the case of pure cubic extensions, i.e. a = 0 and b ∈ k∖k³. We prove that if deg f = 4 and contains a k-rational point (x₀,y₀,z₀,t₀) with f(t₀)≠0, then is k-unirational. A similar result is proved for a broad family of quintic polynomials f satisfying...
Rational torsion points on elliptic curves over number fields
Rational torsion points on Jacobians of modular curves
Let p be a prime greater than 3. Consider the modular curve X₀(3p) over ℚ and its Jacobian variety J₀(3p) over ℚ. Let (3p) and (3p) be the group of rational torsion points on J₀(3p) and the cuspidal group of J₀(3p), respectively. We prove that the 3-primary subgroups of (3p) and (3p) coincide unless p ≡ 1 (mod 9) and .
Rational tree morphisms and transducer integer sequences: definition and examples.
Rational triangles with equal area.
Rational values of the arccosine function
We give a short proof to characterize the cases when arccos(√r), the arccosine of the squareroot of a rational number r ∈ [0, 1], is a rational multiple of π: This happens exactly if r is an integer multiple of 1/4. The proof relies on the well-known recurrence relation for the Chebyshev polynomials of the first kind.
Rationale Approximationen am Einheitskreis.
Rationale Punkte auf Fermatkurven und getwisteten Modulkurven.
Rationale Punkte über eine algebraische Kurve (points rationnels sur une courbe algébrique)
Rationale Tetraeder.
Rationalité de valeurs spéciales de certaines fonctions L
Rationality of a certain formal power series attached to local densities of quadratic forms.
Rationals Not Expressible as a Sum of Three Unit Fractions.
Ratios of congruent numbers
Rauzy tilings and bounded remainder sets on the torus.
Ray class fields of global function fields with many rational places
Reading along arithmetic progressions
Given a 0-1 sequence x in which both letters occur with density 1/2, do there exist arbitrarily long arithmetic progressions along which x reads 010101...? We answer the above negatively by showing that a certain regular triadic Toeplitz sequence does not have this property. On the other hand, we prove that if x is a generalized binary Morse sequence then each block can be read in x along some arithmetic progression.
Real characters of the ideal class-group and the narrow ideal class-group of Q(√d)
Real classes in the ultrapower of hereditarily finite sets