相关论文: Dilogarithm identities
Building on results by Abouzahra and Lewin, McIntosh, and Kirilov we derive new functional dilogarithm equations and consequent diologarithim ladders. By showing that the ratio of a pair of sextic and cubic integrals equals a rational…
We introduce dilogarithm identities through a beta integral-based technique that we apply to provide analytic proofs of previously conjectured dilogarithm relations, solving open problems given by both Bytsko and Campbell, and that we…
We give a new interpretation and proof of the dilogarithm identities, associated to the affine Kac-Moody algebra sl(2)^, using the path description of the corresponding crystal basis. We also discuss connections with algebraic K-theory.
A quantum generalization of Rogers' five term, or ``pentagon'' dilogarithm identity is suggested. It is shown that the classical limit gives usual Rogers' identity. The case where the quantum identity is realized in finite dimensional space…
Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms,…
Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the…
Kanade explored the construction of modular companions to $q$-series identities, using the asymptotics of Nahm sums, and Mizuno [Ramanujan J.\ {\bf 66} (2025), Paper No.\ 62, 31] recently obtained a generalization of Kanade's asymptotic…
Recently Cherednik and Feigin obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series of dilogarithm identities, some of which are known, while…
For the whole set of dilogarithm identities found recently using the thermodynamic Bethe-Ansatz for the $ADET$ series of purely elastic scattering theories we give partition identities which involve characters of those conformal field…
We give a new proof of the dilogarithm identities, associated to the (2,2n+1) minimal models of the Virasoro algebra.
We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results…
In arXiv:0912.1346, four quantum dilogarithm identities containing infinitely many factors are proposed as wall-crossing formula for refined BPS invariant. We give algebraic proof of these identities using the formula for universal R-matrix…
Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting…
We conjecture polynomial identities which imply Rogers--Ramanujan type identities for branching functions associated with the cosets $({\cal G}^{(1)})_{\ell-1}\otimes ({\cal G}^{(1)})_{1} / ({\cal G}^{(1)})_{\ell}$, with ${\cal…
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras,…
We study quantum dilogarithm identities for cyclic quivers following Reineke's idea via Ringel-Hall algebra approach. For any given discrete stability function for the cyclic quiver $\Delta_n$ with $n$ vertices, we obtain certain cyclic…
We prove quite general statements about functional equations in any number of variables for the dilogarithms defined by Bloch-Wigner, Rogers, and Coleman, showing that they follow from certain 5-term and 2-term relations in a precise way.…
We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of…
We use the periodicities of cluster groupoid mutations established by Li and the second author to prove that the dilogarithm identities of higher degree obtained by Nakanishi follow from the classical dilogarithm identities associated to a…
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…