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Let $f (x)$ be a power series $\sum_{n \geq 1} ζ (n) x^{e (n)}$ , where $(e (n))$ is a strictly increasing linear recurrence sequence of non-negative integers, and $(ζ (n))$ a sequence of roots of unity in ${\bar{ℚ}}_{p}$ satisfying an appropriate technical condition. Then we are mainly interested in characterizing the algebraic independence over $ℚ_{p}$ of the elements $f (α_{1}), ...,$ $f (...$

Algebraic independence results for reciprocal sums of Fibonacci numbers

Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2011) Acta Arithmetica

Algebraic integers as values of elliptic functions

Daeyeoul Kim, Ja Kyung Koo (2001) Acta Arithmetica

Algebraic integers near the unit circle

P. Blanksby, H. Montgomery (1971) Acta Arithmetica

Algebraic integers of small discriminant

Jeffrey Lin Thunder, John Wolfskill (1996) Acta Arithmetica

Algebraic integers whose conjugates lie near the unit circle

Cameron L. Stewart (1978) Bulletin de la Société Mathématique de France

Algebraic $K$ -theory and sums-of-squares formulas.

Dugger, Daniel, Isaksen, Daniel C. (2005)

Documenta Mathematica

Algebraic K-Theory and Quadratic Forms.

J. MILNOR (1969/1970)

Inventiones mathematicae

Algebraic leaves of algebraic foliations over number fields

Jean-Benoît Bost (2001)

Publications Mathématiques de l'IHÉS

We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field $K$ embedded in $C$ , a smooth algebraic variety $X$ over $K$ , equipped with a $K -$ rational point $P$ , and $F$ an algebraic subbundle of the its tangent bundle $T_{X}$ , defined over $K$ . Assume moreover that the vector bundle $F$ is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold $X (C)$ , and one may consider its leaf $F$ through $P$ . We prove...

Algebraic number fields with the principal ideal condition

Charles Parry (1971)

Acta Arithmetica

Algebraic Numbers

Yasushige Watase (2016)

Formalized Mathematics

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

C. Lloyd-Smith (1985)

Acta Arithmetica

Algebraic points of abelian functions in two variables

Alex Bijlsma (1982)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Algebraic points of low degree on the Fermat quintic

Matthew Klassen, Pavlos Tzermias (1997)

Acta Arithmetica

Algebraic points on cubic hypersurfaces

D. Coray (1976)

Acta Arithmetica

Algebraic properties of a family of Jacobi polynomials

John Cullinan, Farshid Hajir, Elizabeth Sell (2009)

Journal de Théorie des Nombres de Bordeaux

The one-parameter family of polynomials $J_{n} (x, y) = \sum_{j = 0}^{n} (\binom{y + j}{j}) x^{j}$ is a subfamily of the two-parameter family of Jacobi polynomials. We prove that for each $n \geq 6$ , the polynomial $J_{n} (x, y_{0})$ is irreducible over $ℚ$ for all but finitely many $y_{0} \in ℚ$ . If $n$ is odd, then with the exception of a finite set of $y_{0}$ , the Galois group of $J_{n} (x, y_{0})$ is $S_{n}$ ; if $n$ is even, then the exceptional set is thin.

Algebraic relations between special values of multiple sine functions

Hidekazu Tanaka (2009)

Acta Arithmetica

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