14 citations · 98 across the 24 of their papers we have counts for
6 papers · 1 filter
O-minimality on twisted universal torsors and Manin's conjecture over number fields
Christopher Frei, Marta Pieropan
Manin's conjecture predicts the distribution of rational points on Fano varieties. Using explicit parameterizations of rational points by integral points on universal torsors and l…
Sums of units in function fields II - The extension problem
Christopher Frei
In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated…
Sums of units in function fields
Christopher Frei
Let R be the ring of S-integers of an algebraic function field (in one variable) over a perfect field, where S is finite and not empty. It is shown that for every positive integer…
On sums of S-integers of bounded norm
Christopher Frei, Robert F. Tichy, Volker Ziegler
We prove an asymptotic formula for the number of S-integers in a number field K that can be represented by a sum of n S-integers of bounded norm.
Counting imaginary quadratic points via universal torsors, II
Ulrich Derenthal, Christopher Frei
We prove Manin's conjecture for four singular quartic del Pezzo surfaces over imaginary quadratic number fields, using the universal torsor method.
Counting imaginary quadratic points via universal torsors
Ulrich Derenthal, Christopher Frei
A conjecture of Manin predicts the distribution of rational points on Fano varieties. We provide a framework for proofs of Manin's conjecture for del Pezzo surfaces over imaginary…