Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev Points

The coordinate algebras of quantum groups at pα-th roots of unity are finite modules over their centers, at least in a suitable completed sense (cf. [E]). We describe their centers in the completed case, and deduce from this the centers of the non-completed algebras. As in the [dCKP] situation, it is generated by its “Poisson” and “Frobenius” parts.

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Comonotone and coconvex rational interpolation and approximation

Numerical Algorithms ◽

10.1007/s11075-010-9445-2 ◽

2011 ◽

Vol 58 (1) ◽

pp. 1-21 ◽

Cited By ~ 6

Author(s):

Hoa Thang Nguyen ◽

Annie Cuyt ◽

Oliver Salazar Celis

Keyword(s):

Rational Interpolation

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XI. Analysis of the roots of equations

Philosophical Transactions of the Royal Society of London ◽

10.1098/rstl.1837.0013 ◽

1837 ◽

Vol 127 ◽

pp. 161-178

Keyword(s):

Roots Of Unity ◽

Constituent Part ◽

Roots Of Equations

1. The object of this memoir is to show how the constituent parts of the roots of algebraical equations may be determined, by considering the conditions under which they vanish, and conversely to show the signification of each such constituent part. 2. In equations of degrees higher than the second the same constituent part of the root is found in several places governed by the same radical sign, but affected with the different corresponding roots of unity as multipliers.

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IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/aicu-2013-0006 ◽

2014 ◽

Vol 60 (1) ◽

pp. 19-36

Author(s):

Dae San Kim

Keyword(s):

Generating Function ◽

Bernoulli Polynomials ◽

Roots Of Unity ◽

Integral Expression ◽

Power Sums ◽

Exponential Generating Function

Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

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