arXiv subjects

Jonah Sinick

Publications and source records attributed to Jonah Sinick.

2 recordsLinked to original sources

arXiv2010

Real Places and Surface Bundles

Our results complement D. Calegari's result that there are no hyperbolic once-punctured torus bundles over $S^1$ with trace field having real place. We exhibit several infinite families of pairs $(-χ, p)$ such that there exist hyperbolic surface bundles with over $S^1$ with fiber having $p$ punctures and Euler characteristic $χ$ with trace field of having a real place. This supports our conjecture that there exist such examples for each pair $(-χ, p)$ with finitely many known exceptions.

math.GT↗

arXiv2009

Ramanujan congruences for a class of eta quotients

We consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes $\ell$ for which their coefficients $c(n)$ obey congruences of the form $c(\ell n + a) \equiv 0 \pmod \ell$. We apply this result to obtain a complete characterization of the congruences of the same form that the sequences $c_N(n)$ satisfy, where $c_N(n)$ is defined by $ \sum_{n=0}^{\infty} c_N(n)q^n = \prod_{n=1}^{\infty} \frac{1}{(1-q^n)(1-q^{Nn})}$. This last result answers a question of H.-C. Chan.

math.NT↗