19 citations · 44 across the 11 of their papers we have counts for
12 papers
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 a uniform bound for exponential sums modulo for Deligne polynomials
Kien Huu Nguyen
Let be a polynomial of degree in variables over . Let be the homogeneous part of degree of and be the dimension of the critical locus of…
A Pila--Wilkie theorem for Hensel minimal curves
Victoria Cantoral-Farfán, Kien Huu Nguyen, Mathias Stout +1
Recently, a new axiomatic framework for tameness in henselian valued fields was developed by Cluckers, Halupczok, Rideau-Kikuchi and Vermeulen and termed Hensel minimality. In this…
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…
Combining Igusa's conjectures on exponential sums and monodromy with semi-continuity of the minimal exponent
Raf Cluckers, Kien Huu Nguyen
We combine two of Igusa's conjectures with recent semi-continuity results by Mustaţă and Popa to form a new, natural conjecture about bounds for exponential sums. These bounds have…
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…
Uniform rationality of the Poincaré series of definable, analytic equivalence relations on local fields
Kien Huu Nguyen
Poincaré series of -adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations…
An example of a -minimal structure without definable Skolem functions
Pablo Cubides Kovacsics, Kien Huu Nguyen
We show there are intermediate -minimal structures between the semi-algebraic and sub-analytic languages which do not have definable Skolem functions. As a consequence, by a res…