SICs and Algebraic Number Theory
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DOI: 10.1007/s10701-017-0090-7
Abstract: We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible… read more here.
Keywords: sics algebraic; algebraic number; number theory;
On the distribution of norm groups in the intervals corresponding to odd degree extensions of algebraic number fields
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DOI: 10.1080/00927872.2018.1492586
Abstract: Abstract Let X be a subgroup of a group Y. The interval (X, Y) is the set of subgroups of Y that contain X including X and Y. Let K/k be a finite extension of… read more here.
Keywords: algebraic number; number fields; extensions algebraic; number ... See more keywords
Cyclotomic Quotients of Two Conjugates of an Algebraic Number
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DOI: 10.1134/s0037446621030034
Abstract: Let $ \alpha $ be an algebraic number of degree $ d\geq 2 $ . We consider the set $ E(\alpha) $ of positive integers $ n $ such that the primitive $ n $… read more here.
Keywords: number; algebraic number; conjugates algebraic; two conjugates ... See more keywords
Ramanujan’s sum in the ring of integers of an algebraic number field
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DOI: 10.1142/s1793042120500037
Abstract: In this paper, we generalize Ramanujan’s sum to the ring of integers of an algebraic number field. We also obtain the orthogonality properties of Ramanujan’s sum in the ring of integers. read more here.
Keywords: algebraic number; ring integers; ramanujan sum; sum ring ... See more keywords