Assuming that $\zeta(s)$ has no nontrivial zero with $\mathrm{Re}\, s>7/8$, as asserted in a recent unrefereed preprint of OpenAI, we obtain $\Lambda \le 13963/100000 = 0.13963$ for the de Bruijn-Newman constant. A published Polymath boundary computation supplies a finite-region strip of half-width $1/5$. We derive an...
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 $T_{31A}$ through the classical Rogers--Ramanujan function $U(1,31)$. A theta dissection directly derives the modular target. For the underlying quad...
Let $F$ be a rank-two symmetrizable Nahm sum, with any symmetrizer $\operatorname{diag}(d_1,d_2)$, a positive-definite rational matrix and rational shifts, and let $K$ be the field generated by its Nahm point; write $m=d_2/d_1$. We prove that if $q^cF$ is modular, then $[K:\mathbb{Q}]\le 24$. Modularity forces the high...
We evaluate the series $\sum_{n\ge1} z^n\big/\!\big(n^2\binom{4n}{n}\big)$, equal to $-\tfrac{z}{4}\,{}_5F_4\!\left(1,1,1,\tfrac43,\tfrac53;\tfrac54,\tfrac32,\tfrac74,2;\tfrac{27z}{256}\right)$, in closed form at an infinite family of algebraic points indexed by a rational angle $\theta=j\pi/N$. Each value equals $c\,\...
Cetin Hakimoglu-Brown· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
