https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 Evaluation of triple Euler sums https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13001 Wed 11 Apr 2018 14:09:36 AEST ]]> Special values of multiple polylogarithms https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12998 Wed 11 Apr 2018 13:18:11 AEST ]]> Explicit evaluation of Euler sums https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14235 h(s,t) can be evaluated in terms of Riemann ζ-functions when s + t is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we give a formula for the series [unable to replicate formula]. This evaluation involves ζ-functions and σ_h(2,m).]]> Wed 11 Apr 2018 10:48:46 AEST ]]> On an intriguing integral and some series related to ζ (4) https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13011 Wed 11 Apr 2018 09:15:09 AEST ]]> Many values of the Riemann zeta function at odd integers are irrational https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:33002 s are irrational, where ε is any positive real number and s is large enough in terms of ε. This improves on the lower bound [formula could not be replicated] log s that follows from the Ball-Rivoal theorem. We give the main ideas of the proof, which is based on an elimination process between several linear forms in odd zeta values with related coefficients.]]> Tue 03 Sep 2019 18:00:24 AEST ]]> Algebraic relations for multiple zeta values https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11933 Sat 24 Mar 2018 11:09:03 AEDT ]]> On the residue class distribution of the number of prime divisors of an integer https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31341 n) denote the number of prime divisors of n counting multiplicity. One can show that for any positive integer m and all j = 0,1,…,m – 1, we have #{n ≤ x : Ω(n) ≡ j(modm} = x/m + o(x^α), with α = 1. Building on work of Kubota and Yoshida, we show that for m > 2 and any j = 0,1,…,m – 1, the error term is not o(x^α) for any α < 1.]]> Sat 24 Mar 2018 08:44:37 AEDT ]]> Experimental evaluation of Euler series https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:14064 Sat 24 Mar 2018 08:22:33 AEDT ]]> On Eulerian log-gamma integrals and Tornheim–Witten zeta functions https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12922 n = ∫₀¹logⁿΓ(x)dx for 1≤n≤4 and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right]]> Sat 24 Mar 2018 08:18:13 AEDT ]]> Empirically determined Apéry-like formulae for ζ(4n+3) https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13102 Sat 24 Mar 2018 08:15:12 AEDT ]]> Experimental determination of Apéry-like identities for ζ(2n + 2) https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:6476 Sat 24 Mar 2018 07:47:10 AEDT ]]> On Eulerian log-gamma integrals and Tornheim-Witten zeta functions https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:22779 Sat 24 Mar 2018 07:12:15 AEDT ]]>