6 papers · 1 filter
Two-term dilogarithms, mixed-base Nahm sums, and Fricke symmetry
Cetin Hakimoglu-Brown
We study the arithmetic constraints that two-term Rogers dilogarithm relations impose on rank-two Nahm systems with mixed denominator steps. Monomial complement equations give a un…
A Fricke transformation for cubic-residue eta products of level 13
Cetin Hakimoglu-Brown
We prove an explicit Fricke transformation for the two-dimensional space generated by normalized reciprocal products on the cubic-residue cosets modulo 13. The transformation matri…
Collapsing Fifty Dilogarithm Arguments to Five Terms over
Cetin Hakimoglu-Brown
We give a one-parameter functional equation for the real Rogers dilogarithm, with arguments in , and prove it by an explicit array of ten i…
evaluations and a family of identities
Cetin Hakimoglu-Brown
We evaluate the series , equal to $-\tfrac{z}{4}\,{}_5F_4\!\left(1,1,1,\tfrac43,\tfrac53;\tfrac54,\tfrac32,\tfrac74,2;\tfrac{27z}…
On a conjecture due to Kanade related to Nahm sums
Cetin Hakimoglu-Brown
Kanade explored the construction of modular companions to -series identities, using the asymptotics of Nahm sums, and Mizuno [Ramanujan J. 66 (2025), Article 62, 31 pp.] recentl…
Analytic Dilogarithm Identities
Cetin Hakimoglu-Brown
We introduce dilogarithm identities through a beta integral-based technique that we apply to provide analytic proofs of previously conjectured dilogarithm relations, solving open p…