Cetin Hakimoglu-Brown

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math.NT2026

Collapsing Fifty Dilogarithm Arguments to Five Terms over $Q (u, 4 - 3 u^{2})$

Cetin Hakimoglu-Brown

We give a one-parameter functional equation for the real Rogers dilogarithm, with arguments in $Q (u, 4 - 3 u^{2})$ , and prove it by an explicit array of ten i…

math.NT2026

$_{5} F_{4}$ evaluations and a family of $π^{2} + lo g^{2}$ identities

Cetin Hakimoglu-Brown

We evaluate the series $\sum_{n \geq 1} z^{n} / (n^{2} (n 4 n))$ , equal to $-\tfrac{z}{4}\,{}_5F_4\!\left(1,1,1,\tfrac43,\tfrac53;\tfrac54,\tfrac32,\tfrac74,2;\tfrac{27z}…

math.NT2026

On a conjecture due to Kanade related to Nahm sums

Cetin Hakimoglu-Brown

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] r…

math.NT2025

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…

Collapsing Fifty Dilogarithm Arguments to Five Terms over Q(u,4−3u2​)

5​F4​ evaluations and a family of π2+log2 identities

On a conjecture due to Kanade related to Nahm sums

Analytic Dilogarithm Identities

Collapsing Fifty Dilogarithm Arguments to Five Terms over $Q (u, 4 - 3 u^{2})$

$_{5} F_{4}$ evaluations and a family of $π^{2} + lo g^{2}$ identities