7 papers
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}…
Functional Dilogarithm Identities in Quadratic Fields
Cetin Hakimoglu-Brown
We derive three- and six-term functional dilogarithm identities whose arguments lie in and . Our approach is based on an…
On a -identity due to Gosper
Cetin Hakimoglu-Brown
It is only in exceptional cases that a -series with rational parameters and a rational argument, apart from the cases for associated with…
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…