Leonhard Hochfilzer

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20192024

most citedRatios of Artin L-functions

1 citations · 1 across the 7 of their papers we have counts for

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math.NT2024

Rational points on del Pezzo surfaces of low degree

Jakob Glas, Leonhard Hochfilzer

We give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is n…

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…

math.NT2021

Variance of sums in short intervals and $L$ -functions in $F_{q} [t]$

Leonhard Hochfilzer

Keating and Rudnick studied the variance of the polynomial von Mangoldt function $Λ : F_{q} [t] \to C$ in arithmetic progressions and short intervals usi…

math.NT2019★ 1 cited

Ratios of Artin L-functions

Leonhard Hochfilzer, Thomas Oliver

We show that certain quotients of Artin L-functions have infinitely many poles. Our result follows from a converse theorem for Maass forms of Laplace eigenvalue 1/4 in which the tw…

Rational points on del Pezzo surfaces of low degree

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)

Variance of sums in short intervals and L-functions in Fq​[t]

Ratios of Artin L-functions

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

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

Variance of sums in short intervals and $L$ -functions in $F_{q} [t]$