A Logarithmic Transcendent

Sandham, H. F.

doi:10.1112/jlms/s1-24.2.83b

Cited by 12 publications

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“…Indeed, in this case, exactly two of the 10 foliations defined by the functions appearing in (70) coincide thus W S 2 is a 9-web; second, the intrinsic dimension of the latter is 2 hence it is the pull-back of a planar 9-web that we denote by W ′ S 2 . In this case, Sandam has established (see [Sand,§8] or [Lew1,§6.8 3) is equivalent to the following identity for the classical trilogarithm Li 3 : 63 We have verified this only for N = 3. which is identically verified under the assumption that the variables X, Y and Z satisfy the algebraic relation X + Y + Z = XYZ. Up to a birational change of coordinates, it can be seen that the previous identity is equivalent to the Spence-Kummer equation (SK) (cf.…”

Section: 2313mentioning

confidence: 69%

On webs, polylogarithms and cluster algebras

Pirio

2021

Preprint

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In this text, we investigate webs which can be associated to cluster algebras from the point of view of the abelian functional equations these webs carry, focusing on the polylogarithmic ones. We introduce a general notion of webs whose rank is 'As Maximal as Possible' (AMP) and show that many webs associated either to polylogarithmic functional equations or to cluster algebras are of this type. In particular, we prove a few results and state some conjectures about cluster webs associated to (pairs of) Dynkin diagrams. Along the way, we show that many of the classical functional equations satisfied by low-order polylogarithms (such as Spence-Kummer's equation of the trilogarithm or the tetralogarithmic one of Kummer) are of cluster type.

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Section: 2313mentioning

confidence: 69%

On webs, polylogarithms and cluster algebras

Pirio

2021

Preprint

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“…There are many directions which could be pursued. One is to try to use the generalization by Sandham [8] of the methods of Rogers to obtain identities similar to (3k) with trilogarithms instead of dilogarithms. The resulting relations would undoubtably be extremely complicated and further progress is intimately tied to an old unsolved problem of finding functional equations for general polylogarithms.…”

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confidence: 99%

Relations Between Mahler's Measure and Values of L-Series

Ray

1987

Can. j. math.

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Mahler's measure is a natural generalization of Jensen's formula to polynomials in several variables. Its definition is as follows:The importance of Mahler's measure for polynomials in several variables lies in its connection to Lehmer's classical question which can be phrased in terms of Mahler's measure for polynomials in one variable:Given , are there any polynomials p with integer coefficients in one variable for which ?Surprisingly, Boyd [1] has shown that to answer this question, it is necessary to investigate the larger question involving polynomials in several variables.

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Zur zweiten störungstheoretischen Näherung der Meson‐Nukleon‐Streuung

Weber

1953

Annalen der Physik

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A Logarithmic Transcendent

Cited by 12 publications

References 0 publications

On webs, polylogarithms and cluster algebras

On webs, polylogarithms and cluster algebras

Relations Between Mahler's Measure and Values of L-Series

Zur zweiten störungstheoretischen Näherung der Meson‐Nukleon‐Streuung

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