Leonhard Hochfilzer

collaborators

4 papers

math.NT2023

Cubic forms over imaginary quadratic number fields and pairs of rational cubic forms

Christian Bernert, Leonhard Hochfilzer

We show that every cubic form with coefficients in an imaginary quadratic number field $K / Q$ in at least $14$ variables represents zero non-trivially. This builds on the c…

math.NT2023

On Artin's Primitive Root Conjecture for Function Fields over $F_{q}$

Leonhard Hochfilzer, Ezra Waxman

In 1927, E. Artin proposed a conjecture for the natural density of primes $p$ for which $g$ generates $(Z / p Z)^{\times}$ . By carefully observing numerical deviations…

math.NT2023

Systems of bihomogeneous forms of small bidegree

Leonhard Hochfilzer

We use the circle method to count the number of integer solutions to systems of bihomogeneous equations of bidegree $(1, 1)$ and $(2, 1)$ of bounded height in lopsided boxes. Previou…

math.NT2022

On a question of Davenport and diagonal cubic forms over $F_{q} (t)$

Jakob Glas, Leonhard Hochfilzer

Given a non-singular diagonal cubic hypersurface $X \subset P^{n - 1}$ over $F_{q} (t)$ with $char (F_{q}) \neq = 3$ , we show that the number of rational po…

Cubic forms over imaginary quadratic number fields and pairs of rational cubic forms

On Artin's Primitive Root Conjecture for Function Fields over Fq​

Systems of bihomogeneous forms of small bidegree

On a question of Davenport and diagonal cubic forms over Fq​(t)

On Artin's Primitive Root Conjecture for Function Fields over $F_{q}$

On a question of Davenport and diagonal cubic forms over $F_{q} (t)$