https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:28429 Wed 11 Apr 2018 16:31:28 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12969 0, x, y are real numbers and Odenotes the odd integers. In this paper we first survey the earlier work and then discuss the sum (1) more completely. Conclusions: As in the previous study, we find some surprisingly simple closed-form evaluations of these sums. In particular, we find that in some cases these sums are given by 1/π logA, where A is an algebraic number. These evaluations suggest that a deep theory interconnects all such summations.]]> Wed 11 Apr 2018 09:47:17 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12924 n(r₁,...,r_n) = 1/π²[formula could not be replicated]. By virtue of striking connections with Jacobi ϑ-function values, we are able to develop new closed forms for certain values of the coordinates r_k, and extend such analysis to similar lattice sums. A primary result is that for rational x, y, the natural potential ⏀²(x, y) is 1/π log A where A is an algebraic number. Various extensions and explicit evaluations are given. Such work is made possible by number-theoretical analysis, symbolic computation and experimental mathematics, including extensive numerical computations using up to 20,000-digit arithmetic.]]> Sat 24 Mar 2018 10:37:10 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:32483 Mon 23 Sep 2019 10:10:28 AEST ]]>