Quantum groups and zeta-functions
Kimio Ueno, Michitomo Nishizawa
TL;DR
This paper introduces a $q$-analogue of the Hurwitz zeta-function derived from quantum group spectral analysis, exploring its properties and asymptotic behavior using advanced summation techniques.
Contribution
It presents a novel $q$-analogue of the Hurwitz zeta-function based on quantum group $SU_q(2)$ spectral data and analyzes its analytic properties and asymptotics.
Findings
Defined a new $q$-analogue of the Hurwitz zeta-function
Studied the analytic properties using Euler-MacLaurin formula
Derived asymptotic formulas for related $q$-functions
Abstract
A -analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group , and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas of some relevant -functions are discussed.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Mathematical Theories and Applications · Graph theory and applications