Algebraic independence of the values of Mahler functions satisfying implicit functional equations
Algebraic independence of the values of power series generated by linear recurrences
Algebraic Independence of Values of Elliptic Functions.
Algebraic independence over
Let be a power series , where is a strictly increasing linear recurrence sequence of non-negative integers, and a sequence of roots of unity in satisfying an appropriate technical condition. Then we are mainly interested in characterizing the algebraic independence over of the elements
Algebraic independence results for reciprocal sums of Fibonacci numbers
Algebraic integers as values of elliptic functions
Algebraic integers near the unit circle
Algebraic integers of small discriminant
Algebraic integers whose conjugates lie near the unit circle
Algebraic -theory and sums-of-squares formulas.
Algebraic K-Theory and Quadratic Forms.
Algebraic leaves of algebraic foliations over number fields
We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field embedded in , a smooth algebraic variety over , equipped with a rational point , and an algebraic subbundle of the its tangent bundle , defined over . Assume moreover that the vector bundle is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold , and one may consider its leaf through . We prove...
Algebraic number fields with the principal ideal condition
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 points of abelian functions in two variables
Algebraic points of low degree on the Fermat quintic
Algebraic points on cubic hypersurfaces
Algebraic properties of a family of Jacobi polynomials
The one-parameter family of polynomials is a subfamily of the two-parameter family of Jacobi polynomials. We prove that for each , the polynomial is irreducible over for all but finitely many . If is odd, then with the exception of a finite set of , the Galois group of is ; if is even, then the exceptional set is thin.
Algebraic relations between special values of multiple sine functions