In the finite-temperature Yang-Mills theory we calculate the functional determinant for fermions in the fundamental representation of SU(N) gauge group in the background of an instanton with non-trivial holonomy at spatial infinity. This object, called the Kraan–van Baal – Lee–Lu caloron, can be viewed as composed of N Bogomolny–Prasad–Sommerfeld monopoles (or dyons). We compute analytically tw...

Research supported by the Natural Sciences and Engineering Research Council (Canada) and Fonds pour la Formation de Chercheurs et l'Aide a la Recherche (Quebec). Some results in section 3 of this work are taken from Jha's Ph.D. thesis [Jha 1992]. After a brief review of partial results regarding Case I of Fermat’s Last Theorem, we discuss the relationship between the number of points on Fermat’...

Adapting a method used by Cauchy, Bailey, Slater, and more recently, the second author, we give a new proof of Bailey’s celebrated 6ψ6 summation formula.

In the paper, the authors find a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.