scholarly journals Special values of finite multiple harmonic $q$-series at roots of unity

2020 ◽  
pp. 1-18
Author(s):  
Henrik Bachmann ◽  
Yoshihiro Takeyama ◽  
Koji Tasaka
Keyword(s):  
Roots Of Unity ◽  
Special Values

Asymptotic expansions, partial theta functions, and radial limit differences of mock modular and modular forms

2020 ◽  
pp. 1-10
Author(s):  
Amanda Folsom
Keyword(s):  
Theta Function ◽  
Modular Forms ◽  
Asymptotic Expansions ◽  
Theta Functions ◽  
Roots Of Unity ◽  
Radial Limit ◽  
Special Values ◽  
Partial Theta Function ◽  
Finite Sums ◽  
Partial Theta Functions

In 1920, Ramanujan studied the asymptotic differences between his mock theta functions and modular theta functions, as [Formula: see text] tends towards roots of unity singularities radially from within the unit disk. In 2013, the bounded asymptotic differences predicted by Ramanujan with respect to his mock theta function [Formula: see text] were established by Ono, Rhoades, and the author, as a special case of a more general result, in which they were realized as special values of a quantum modular form. Our results here are threefold: we realize these radial limit differences as special values of a partial theta function, provide full asymptotic expansions for the partial theta function as [Formula: see text] tends towards roots of unity radially, and explicitly evaluate the partial theta function at roots of unity as simple finite sums of roots of unity.

scholarly journals MULTI-POLYLOGS AT TWELFTH ROOTS OF UNITY AND SPECIAL VALUES OF WITTEN MULTIPLE ZETA FUNCTION ATTACHED TO THE EXCEPTIONAL LIE ALGEBRA 𝔤2

2010 ◽  
Vol 09 (02) ◽  
pp. 327-337 ◽  
Author(s):  
JIANQIANG ZHAO
Keyword(s):  
Zeta Function ◽  
Lie Algebra ◽  
Roots Of Unity ◽  
Linear Combinations ◽  
Exceptional Lie Algebra ◽  
Special Values ◽  
Multiple Zeta Function ◽  
Multiple Zeta

In this note, we shall study the Witten multiple zeta function associated with the exceptional Lie algebra 𝔤2. Our main result shows that its special values at nonnegative integers can always be expressed as rational linear combinations of the multi-polylogs evaluated at 12th roots of unity, except for two irregular cases.

Hermite-Birkhoff Interpolation in the nth Roots of Unity

1980 ◽  
Vol 259 (2) ◽  
pp. 621 ◽  
Author(s):  
A. S. Cavaretta ◽  
A. Sharma ◽  
R. S. Varga
Keyword(s):  
Roots Of Unity ◽  
Birkhoff Interpolation

THE CENTER OF THE COORDINATE ALGEBRAS OF QUANTUM GROUPS AT pα-th ROOTS OF UNITY

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3547-3550
Author(s):  
BENJAMIN ENRIQUEZ
Keyword(s):  
Quantum Groups ◽  
Roots Of Unity

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.

scholarly journals XI. Analysis of the roots of equations

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.

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

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.

Special Values of L-Series

1992 ◽  
Vol 114 (2) ◽  
pp. 337 ◽  
Author(s):  
Rhonda L. Hatcher
Keyword(s):  
Special Values
Sign in / Sign up

Export Citation Format

Share Document