7 papers
Corrigendum to `Evaluation of motivic functions, non-nullity, and integrability in fibers', Advances in Mathematics, Vol. 409, Part A, Paper No. 108635, 29 pages, doi:10.1016/j.aim.2022.108635 (2022)
Raf Cluckers, Immanuel Halupczok
We correct the statements and proofs of the (auxiliary) Propositions 4.1 and 4.2 of our paper `Evaluation of motivic functions, non-nullity, and integrability in fibers' in Advance…
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…
Analytic holonomicity of real C-class distributions
Avraham Aizenbud, Raf Cluckers, Michel Raibaut +1
We introduce a notion of distributions on , called distributions of C-class, based on wavelet transforms of distributions and the theory from Clucker…
Improvements on dimension growth results and effective Hilbert's irreducibility theorem
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel +2
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree , over any global field. In…
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…
Sharp bounds for the number of rational points on algebraic curves and dimension growth, over all global fields
Gal Binyamini, Raf Cluckers, Fumiharu Kato
Let be an algebraic curve over a number field , and denote by the degree of over . We prove that the number of -rational poin…