6 papers
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…
-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…
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…
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…
On single-variable Witten zeta functions of rank two and three
Kam Cheong Au
By introducing a novel integration kernel for Mellin transform, we uncover many previously unknown and intriguing properties of the Witten zeta functions of rank two and three. Det…
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 re…