https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Neverending fractions: an introduction to continued fractions https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17585 Wed 17 Jun 2015 08:22:10 AEST ]]> Hankel determinants of zeta values https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:25545 Wed 11 Apr 2018 17:10:43 AEST ]]> On the (K.2) supercongruence of Van Hamme https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:23974 Wed 11 Apr 2018 15:39:12 AEST ]]> Algebraic independence of Mahler functions via radial asymptotics https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:23973 2)F(z4) +z4F(z16)=0. Specifically, we prove that the functions F(z), F(z4), F′(z), and F′(z4) are algebraically independent over ℂ(z). An application of a celebrated result of Ku. Nishioka then allows one to replace ℂ(z) by ℚ when evaluating these functions at a nonzero algebraic number α in the unit disc.]]> Wed 11 Apr 2018 15:22:41 AEST ]]> On the irrationality of generalized q-logarithm https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:26657 1, and generic rational x and z, we establish the irrationality of the series [formula could not be replicated].It is a symmetric (ℓp(x,z)=ℓp(z,x)) generalization of the q-logarithmic function (x = 1 and p = 1/q where |q|<1), which in turn generalizes the q-harmonic series (x = z = 1). Our proof makes use of the Hankel determinants built on the Padé approximations to ℓp(x,z).]]> Wed 11 Apr 2018 15:04:15 AEST ]]> Multiple q-zeta brackets https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:26481 Wed 11 Apr 2018 14:41:18 AEST ]]> Positivity of rational functions and their diagonals https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:25709 Wed 11 Apr 2018 10:52:53 AEST ]]> On the Mahler measure of a family of genus 2 curves https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27595 Wed 11 Apr 2018 10:35:28 AEST ]]> On the Mahler measure of hyperelliptic families https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:30649 3−y+x3−x+kxy whose zero loci define elliptic curves for k≠0,±3.]]> Wed 11 Apr 2018 09:57:19 AEST ]]> Holonomic alchemy and series for 1/π https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32378 Tue 29 May 2018 13:55:00 AEST ]]> Euler's factorial series and global relations https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:44631 ∞k=0 K! (—z)k, we address arithmetic and analytical questions related to its values in both p-adic and Archimedean valuations.]]> Tue 18 Oct 2022 13:31:37 AEDT ]]> Crouching AGM, hidden modularity https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:37655 Tue 09 Mar 2021 17:58:53 AEDT ]]> 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 ]]> A magnetic double integral https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:44071 Thu 06 Oct 2022 12:11:40 AEDT ]]> Rational approximations to a q-analogue of π and some other q-series. https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:15720 Sat 24 Mar 2018 08:25:20 AEDT ]]> Ramanujan-type formulae for 1/π: a second wind? https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:15765 Sat 24 Mar 2018 08:22:04 AEDT ]]> Two hypergeometric tales and a new irrationality measure of ζ(2) https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:18838 Sat 24 Mar 2018 08:03:20 AEDT ]]> Regulator of modular units and Mahler measures https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:20862 Sat 24 Mar 2018 08:02:52 AEDT ]]> A generating function of the squares of legendre polynomials https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17399 Sat 24 Mar 2018 08:01:28 AEDT ]]> On the Mahler measure of 1+X+1/X+Y +1/Y https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:20722 Sat 24 Mar 2018 08:00:20 AEDT ]]> On simultaneous diophantine approximations to ζ(2) and ζ(3) https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:19583 Sat 24 Mar 2018 07:58:20 AEDT ]]> Apéry limits of differential equations of order 4 and 5. https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:16330 Sat 24 Mar 2018 07:58:01 AEDT ]]> On three theorems of Folsom, Ono and Rhoades https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:27594 Sat 24 Mar 2018 07:25:17 AEDT ]]> On the Mahler measure of a family of genus 2 curves https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:24598 k(x, y)) and m(Pk(x, y)) of two polynomial families, where Qk(x, y) = 0 and Pk(x, y) = 0 are generically hyperelliptic and elliptic curves, respectively.]]> Sat 24 Mar 2018 07:11:48 AEDT ]]> Further explorations of Boyd's conjectures and a conductor 21 elliptic curve https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:24975 a,b,c(x,y)=a(x+1/x)+b(y+1/y)+c] and show that the wanted quantity m(P) is related to a 'half-Mahler' measure of P(x,y)=P √7,1,3(x,y). In the finale, we use the modular parametrization of the elliptic curve P(x,y)=0, again of conductor 21, due to Ramanujan and the Mellit-Brunault formula for the regulator of modular units.]]> Sat 24 Mar 2018 07:09:57 AEDT ]]> A determinantal approach to irrationality https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32649 n/qn with integral pn and qn such that qnξ−pn≠0 for all n and qnξ−pn→0 as n→∞. In this paper, we give an extension of this criterion in the case when the sequence possesses an additional structure; in particular, the requirement qnξ−pn→0 is weakened. Some applications are given, including a new proof of the irrationality of π. Finally, we discuss analytical obstructions to extend the new irrationality criterion further and speculate about some mathematical constants whose irrationality is still to be established.]]> Mon 23 Sep 2019 10:53:04 AEST ]]> A modular supercongruence for ₆F₅: an Apéry-like story https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35952 Mon 20 Jan 2020 13:33:07 AEDT ]]> A study of elliptic gamma function and allies https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35950 Mon 20 Jan 2020 11:48:08 AEDT ]]> A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:42845 Mon 05 Sep 2022 15:05:30 AEST ]]> Ramanujan-type formulae for 1/: q-analogues https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:41268 Mon 01 Aug 2022 09:49:21 AEST ]]> A Variation on the Theme of Nicomachus https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:45501 Fri 28 Oct 2022 16:00:10 AEDT ]]> Linear independence of dilogarithmic values https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35920 Fri 17 Jan 2020 09:08:09 AEDT ]]>