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A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter. In the odd case, int...
Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory
the Borwein-Broadhurst conjecture dilogarithmic integral arising quantum field theory
2010/11/8
Borwein and Broadhurst, using experimental-mathematics techniques, in 1998 identified numerous hyperbolic 3-manifolds whose volumes are rationally related to values of various Dirichlet L series $\te...
Integral Menger curvature for sets of arbitrary dimension in $\mathbb{R}^n$. Part I: Uniform Ahlfors regularity
Integral Menger curvature math
2010/11/15
We propose the notion of integral Menger curvature for $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies Ahlfors regularity with constant depe...