Algebraic independence results for reciprocal sums of Fibonacci numbers
Algebraic integers near the unit circle
Algebraic integers of small discriminant
Algebraic integers whose conjugates lie near the unit circle
Algebraic Numbers
This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to the polynomial...
Algebraic numbers near the unit circle
Algebraic S-integers of fixed degree and bounded height
Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.
Algebraische Abhängigkeit von Wurzeln
Algorithme de Jacobi-Perron dans les corps de nombres de degré 4
An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers.
An arithmetic analogue of Clifford's theorem.
An arithmetic analogue of Clifford's theorem
Number fields can be viewed as analogues of curves over fields. Here we use metrized line bundles as analogues of divisors on curves. Van der Geer and Schoof gave a definition of a function on metrized line bundles that resembles properties of the dimension of , where is a divisor on a curve . In particular, they get a direct analogue of the Rieman-Roch theorem. For three theorems of curves, notably Clifford’s theorem, we will propose arithmetic analogues.
An arithmetic site for the rings of integers of algebraic number fields.
An asymptotic inequality concerning primes in contours for the case of quadratic number fields
Approximation of irrationals.
Approximation Properties of Some Complex Continued Fractions.
Arithmetic Clifford's theorem for Hermitian vector bundles
Arithmetic of the modular function
We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Arithmetical characterizations of divisor class groups. II.
Arithmetics of beta-expansions