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Roots of unity and unreasonable differentiation

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0 Published in 2019 at "Archiv der Mathematik"

DOI: 10.1007/s00013-019-01342-5

Abstract: AbstractWe explore when it is legal to differentiate a polynomial evaluated at a root of unity using modular arithmetic. read more here.

Keywords: unreasonable differentiation; roots unity; unity unreasonable; unity ... See more keywords

Roots of Unity in Orders

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1 Published in 2017 at "Foundations of Computational Mathematics"

DOI: 10.1007/s10208-016-9304-1

Abstract: We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete… read more here.

Keywords: unity orders; cryptology; roots unity;

Representations of quantum groups at roots of unity, Whittaker vectors and q-W algebras

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1 Published in 2018 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.06.007

Abstract: Abstract Let U e ( g ) be the standard simply connected version of the Drinfeld–Jumbo quantum group at an odd m-th root of unity e. The center of U e ( g ) contains… read more here.

Keywords: whittaker vectors; quantum groups; representations quantum; roots unity ... See more keywords

On sums of two and three roots of unity

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1 Published in 2018 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2018.03.017

Abstract: Abstract Let α ≠ 0 be a sum of some k distinct Nth roots of unity, where 2 ≤ k N . In 1986, Myerson raised the following two problems. How small can | α… read more here.

Keywords: sums two; two three; three roots; roots unity ... See more keywords

Morphisms of Butson classes

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1 Published in 2019 at "Linear Algebra and its Applications"

DOI: 10.1016/j.laa.2019.04.020

Abstract: We introduce the concept of a morphism from the set of Butson Hadamard matrices over kth roots of unity to the set of Butson matrices over $\ell$th roots of unity. As concrete examples of such… read more here.

Keywords: butson; butson matrices; butson classes; morphisms butson ... See more keywords

Herzog–Schönheim conjecture, vanishing sums of roots of Unity and convex polygons

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1 Published in 2020 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1924766

Abstract: Abstract Let G be a group and H 1,…,Hs be subgroups of G of indices respectively. In 1974, M. Herzog and J. Schönheim conjectured that if is a coset partition of G, then cannot be… read more here.

Keywords: unity convex; conjecture; roots unity; sch nheim ... See more keywords

Extended T-systems, Q matrices and T-Q relations for $ \newcommand{\e}{{\rm e}} s\ell(2)$ models at roots of unity

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1 Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"

DOI: 10.1088/1751-8121/ab2490

Abstract: The mutually commuting 1 x n fused single and double-row transfer matrices of the critical six-vertex model are considered at roots of unity q = e(i lambda) with crossing parameter lambda = (p'-p)pi/p' a rational… read more here.

Keywords: extended systems; roots unity; systems matrices; transfer matrices ... See more keywords