arXiv subjects
Publications and source records attributed to Alejandro De Las Penas Castano.
For a product $E_1\times E_2$ of two elliptic curves over a $p$-adic field with good supersingular reduction, we produce infinitely many rational equivalences in the Chow group $\mathrm{CH}_0(X)$ of zero cycles via genus 2 covers of $E_1$ and $E_2$. We use this to obtain evidence for a conjecture of Colliot-Thélène about the structure of the Albanese kernel.
Recently, Hong, Mertens, Ono and Zhang proved a conjecture of Căldăraru, He, and Huang that expresses the Taylor series of the modular $j$-function around the elliptic points $i$ and $ρ=e^{πi/3}$ as rational functions arising from the signature 2 and 3 cases of Ramanujan's theory of elliptic functions to alternative bases. We extend these results and give inversion formulas for the $j$-function around $i$ and $ρ$ arising from Gauss' hypergeometric functions and Ramanujan's theory in signatures 4 and 6.