Cetin Hakimoglu-Brown

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20222026

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math.NT2026

A conditional bound $Λ \leq 0.13963$ for the de Bruijn--Newman constant

Cetin Hakimoglu-Brown

Assuming that $ζ (s)$ has no nontrivial zero with $Re s > 7/8$ , as asserted in a recent unrefereed preprint of OpenAI, we obtain $Λ \leq 13963/100000 = 0.13963$ for the de…

math.NT2026

A uniform degree bound for modular rank-two Nahm sums

Cetin Hakimoglu-Brown

Let $F$ be a rank-two symmetrizable Nahm sum, with any symmetrizer $diag (d_{1}, d_{2})$ , a positive-definite rational matrix and rational shifts, and let $K$ be the field…

math.NT2026

Rank-two Nahm sums, modularity obstructions, and the McKay--Thompson series $T_{31 A}$

Cetin Hakimoglu-Brown

We conjecture a positive four-shift identity for rank-two Nahm sums with denominator steps $(1, 31)$ , giving a mixed-base realization of the Monster McKay--Thompson series $T_{31 A}$ …

math.NT2026

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…

math.NT2026

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…

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.CA2026

Functional Dilogarithm Identities in Quadratic Fields

Cetin Hakimoglu-Brown

We derive three- and six-term functional dilogarithm identities whose arguments lie in $Q (u, 4 - 3 u^{2})$ and $Q (u, u (4 - 3 u))$ . Our approach is based on an…

math.CA2026

On a $_{2} F_{1} (\frac{1}{4})$ -identity due to Gosper

Cetin Hakimoglu-Brown

It is only in exceptional cases that a $_{2} F_{1} (z)$ -series with rational parameters and a rational argument, apart from the cases for $z \in {\pm 1, \frac{1}{2}}$ associated with…

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. 66 (2025), Article 62, 31 pp.] recentl…

A conditional bound Λ≤0.13963 for the de Bruijn--Newman constant

A uniform degree bound for modular rank-two Nahm sums

Rank-two Nahm sums, modularity obstructions, and the McKay--Thompson series T31A​

Two-term dilogarithms, mixed-base Nahm sums, and Fricke symmetry

A Fricke transformation for cubic-residue eta products of level 13

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

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

Functional Dilogarithm Identities in Quadratic Fields

On a 2​F1​(41​)-identity due to Gosper

On a conjecture due to Kanade related to Nahm sums

A conditional bound $Λ \leq 0.13963$ for the de Bruijn--Newman constant

Rank-two Nahm sums, modularity obstructions, and the McKay--Thompson series $T_{31 A}$

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

On a $_{2} F_{1} (\frac{1}{4})$ -identity due to Gosper