Geography

Elphinstone, Mountstuart

doi:10.1017/cbo9781139507622.017

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The General Methods1

A Chebyshev Rearrangement1

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2015

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Cited by 2 publications

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“…2 It is amusing to note that the product formula of Juhl, [7] lemma 6.1, is the central version of Elphinstone's theorem of 1858, [8]. 3 There is one for the hemisphere.…”

Section: The General Methodsmentioning

confidence: 99%

Evaluation of spherical GJMS determinants

Dowker

Mansour

2015

Journal of Geometry and Physics

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An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd-dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. This is formalised and expanded by an analytical treatment of the integral which produces an explicit combinatorial expression directly in terms of the Riemann zeta function, and log 2. An incidental byproduct is a (known) expression for the central factorial coefficients in terms of higher Bernoulli numbers.

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“…2 It is amusing to note that the product formula of Juhl, [7] lemma 6.1, is the central version of Elphinstone's theorem of 1858, [8]. 3 There is one for the hemisphere.…”

Section: The General Methodsmentioning

confidence: 99%

Evaluation of spherical GJMS determinants

Dowker

Mansour

2015

Journal of Geometry and Physics

View full text Add to dashboard Cite

show abstract

“…Steffensen, [22]. It is amusing to note that the product formula of Juhl, [14, Lemma 6.1], is the central version of Elphinstone's theorem of 1858, [11]. 2 There is one for the hemisphere 3 This is a consequence of the appearance of negative eigenvalues of B − α j but this will not be remedied here.…”

Section: A Chebyshev Rearrangementmentioning

confidence: 99%