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Open AccessArticle

Reflection Identities of Harmonic Sums of Weight Four

Department of Physics, Ariel University, Ariel 40700, Israel
Universe 2019, 5(3), 77; https://doi.org/10.3390/universe5030077
Received: 4 January 2019 / Revised: 14 February 2019 / Accepted: 1 March 2019 / Published: 11 March 2019
In attempt to find a proper space of function expressing the eigenvalue of the color-singlet BFKL equation in N = 4 SYM, we consider an analytic continuation of harmonic sums from positive even integer values of the argument to the complex plane. The resulting meromorphic functions have pole singularities at negative integers. We derive the reflection identities for harmonic sums at weight four decomposing a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or non-negative values of the argument. The pole decomposition demonstrates how the product of two simpler harmonic sums can build more complicated harmonic sums at higher weight. We list a minimal irreducible set of bilinear reflection identities at weight four, which represents the main result of the paper. We also discuss how other trilinear and quadlinear reflection identities can be constructed from our result with the use of well known quasi-shuffle relations for harmonic sums. View Full-Text
Keywords: BFKL equation; analytic continuation; Carlson’s theorem; functional identities; harmonic sums BFKL equation; analytic continuation; Carlson’s theorem; functional identities; harmonic sums
MDPI and ACS Style

Prygarin, A. Reflection Identities of Harmonic Sums of Weight Four. Universe 2019, 5, 77.

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