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
Algebraic relations for reciprocal sums of Fibonacci numbers
Algebraic setup of non-strict multiple zeta values
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.
Algebraic systems of quadratic forms of number fields and function fields.
Algebraic values of G-functions.
Algebraic Weyl system and application