4 papers
Integration in Hensel minimal fields
Mathias Stout, Floris Vermeulen
We develop a framework of motivic integration in the style of Hrushovski--Kazhdan in arbitrary Hensel minimal fields of equicharacteristic zero. Hence our work generalizes that of…
Counting rational points on transcendental curves in valued fields
Floris Vermeulen
We prove upper bounds on the number of rational points on transcendental curves in arbitrary -h-minimal fields, similar to the Pila--Wilkie counting theorem in the o-minimal set…
Serre's question on thin sets in projective space
Tijs Buggenhout, Raf Cluckers, Per Salberger +2
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least . For degrees and we improve the known boun…
Motivic Mellin transforms
Raf Cluckers, François Loeser, Kien Huu Nguyen +1
This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with gen…