9 citations · 31 across the 13 of their papers we have counts for
15 papers
Holonomic sequences arising from meromorphic modular forms
Kam Cheong Au
We introduce a systematic framework for constructing holonomic recurrences from meromorphic modular forms. Its central ingredient is a modular analogue of creative telescoping, whi…
Combinatorics of hyperplane arrangements and Witten zeta function at the origin
Kam Cheong Au, Kazuhiro Onodera
We introduce a new method that brings the combinatorics of hyperplane arrangements into the study of representation zeta functions of compact Lie groups. For the Witten zeta functi…
Discovering hypergeometric series with harmonic numbers via Wilf-Zeilberger seeds
Kam Cheong Au
By extracting coefficients from Wilf-Zeilberger pairs with respect to auxiliary parameters, we discover many nontrivial hypergeometric series involving harmonic numbers. In particu…
Linear relations between -values of newforms and moments of elliptic integral
Kam Cheong Au
By systematically translating certain integrals involving moments of the elliptic integral into -values of modular forms on and , and then utilizing relat…
On single-variable Witten zeta functions of rank two and three
Kam Cheong Au
By introducing a novel integration kernel for the Mellin transform, we uncover many previously unknown and intriguing properties of the Witten zeta functions of rank two and three.…
Vanishing of Witten zeta function at negative integers
Kam Cheong Au
We introduce a new analytic method for studying Witten zeta function of a root system , based on a refined manipulation of an integral representation involving the Hurwitz zeta…
Creative telescoping and generating functions of (variants of) multiple zeta values
Kam Cheong Au, Steven Charlton
We show how to convert the generating series of interpolated multiple zeta values, or multiple values, with repeating blocks of length 1 into hypergeometric series. Then we inv…
-analogues of Wilf-Zeilberger seeds and Ramanujan -formulas
Kam Cheong Au
We develop the notion of Wilf-Zeilberger seeds as a powerful framework for generating WZ-pairs and for lifting classical hypergeometric identities to the -setting. As an applica…
Differential operators and a depth reduction for the alternating multiple zeta values
Kam Cheong Au, Steven Charlton, Michael E. Hoffman
We establish an identity amongst certain differential operators applied to a formal power-series. As a corollary we obtain an explicit depth reduction result for alternating MZV's…
Wilf-Zeilberger seeds and non-trivial hypergeometric identities
Kam Cheong Au
Through a systematic approach on generating Wilf-Zeilberger-pairs, we prove some hypergeometric identities conjectures due to Z.W. Sun, J. Guillera and Y. Zhao etc., including two…
Moments of ideal class counting functions
Kam Cheong Au
We consider the counting function of ideals in a given ideal class of a number field of degree . This describes, at least conjecturally, the Fourier coefficients of an automorph…
Multiple zeta values, WZ-pairs and infinite sums computations
Kam Cheong Au
We combine the powerful method of Wilf-Zeilberger pairs with systematic theory of multiple zeta values to prove a large number of series identities due to Z.W. Sun, many of them ha…
Iterated Integrals and Multiple Polylogarithm at Algebraic Arguments
Kam Cheong Au
By introducing a generalized notion of multiple zeta values associated with an arbitrary finite subset and studying their transformation propert…
Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series
Kam Cheong Au
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated inte…
Linear relations between logarithmic integrals of high weight and some closed-form evaluations
K. C. Au
The focus of our investigation will be integrals of form , where can be either or . We show that these integral…