| * Venue | E C G Sudarshan Hall |
| * Speaker | Sonam Garg |
| * Title | On the arithmetic nature of the q-Riemann zeta function and its generalizations |
| Affiliation | IMSc |
| Abstract | Kurokawa and Wakayama (2003) initially introduced a q-analogue of Euler’s constant, exploring the irrationality of certain numbers related to a q-Euler constant. In this talk, we extend their results and study the linear independence properties for certain numbers involving a q-analogue of Euler’s constant. Additionally, we derive the closed-form expression for a q-analogue of the k-th Stieltjes constant, denoted as γk(q). Further, using Nesterenko’s result, we address a question raised by Erdo ̋s in 1948 and using an answer to his question, we discuss the arithmetic nature of some infinite series involving γ1(2). Further, our talk aims to study a q-analogue of the double zeta func- tion. We specifically present a closed-form expression for a q-analogues of Euler’s constant of height 2 (γ0,0(q)), which is the constant term in the Laurent series expansion of a q-analogue of the double zeta function arounds1 =1ands2 =1. Furthermore, we examine the linear independence of a set of numbers involving the constant γ′∗(qi), where 1 ≤ i ≤ r for any integer r ≥ 1. These numbers appear in the Laurent series expansion of a q-double zeta function. Finally, we discuss the irrationality of certain numbers involving a 2-double Euler-Stieltjes constant (γ0,0(2)). |
| * Announcement? | None |
| * Refreshments? | Before the event |
| * Honorarium? | None |
| Special Arrangements? | None |
| * Host name and email |