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On a Conjecture of Gezmis and Pellarin
Khac Nhuan Le, Kien Huu Nguyen
In 2022, Gezmis and Pellarin introduced and studied the concept of trivial multiple zeta values, along with a map from the vector space spanned by these values to the vector space…
Exponential sums and motivic oscillation index of arbitrary ideals and their applications
Kien Huu Nguyen
In 2006, Budur, Mustaţǎ and Saito introduced the notion of Bernstein-Sato polynomial of an arbitrary scheme of finite type over fields of characteristic zero. Because of the strong…
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…