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5 papers
On the motivic oscillation index and bound of exponential sums modulo via analytic isomorphisms
Kien Huu Nguyen, Willem Veys
Let be a polynomial in variables over some number field and a subscheme of affine -space. The notion of motivic oscillation index of at was initiated by Cluc…
The dimension growth conjecture, polynomial in the degree and without logarithmic factors
Wouter Castryck, Raf Cluckers, Philip Dittmann +1
We address Heath-Brown's and Serre's dimension growth conjecture (proved by Salberger), when the degree grows. Recall that Salberger's dimension growth results give bounds of t…
Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities
Raf Cluckers, Mircea Mustaţǎ, Kien Huu Nguyen
We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa's conjecture…
New bounds for exponential sums with a non-degenerate phase polynomial
Wouter Castryck, Kien Huu Nguyen
We prove a recent conjecture due to Cluckers and Veys on exponential sums modulo for in the special case where the phase polynomial is sufficiently non-degener…
Proof of Cluckers-Veys's conjecture on exponential sums for polynomials with log-canonical threshold at most a half
Saskia Chambille, Kien Huu Nguyen
In this paper, we will give two proofs of the Cluckers-Veys conjecture on exponential sums for the case of polynomials in having log-canonical thre…