AbstractIn this paper we compute geometric monodromy groups of additive exponential sums over BbbAn. Our approach builds on work of N. Katz, and involves p-adic analysis of explicit sums and computation of the Galois group of an equation over a function field in characteristic 2. The paper also provides a brief historical outline of the problem and lists previously known results
The main theme of this thesis is the study of compatible systems of $\ell$-adic Galoi...
We prove the remaining part of the conjecture by Denef and Sperber [Denef, J. and Sperber, S., Expon...
Abstract. Let C be a smooth curve over O/plO, O being the valuation ring of an unramified extension ...
AbstractIn this paper we compute geometric monodromy groups of additive exponential sums over BbbAn....
We deduce Katz's theorems for $(A,B)$-exponential sums over finite fields using $\ell$-adic cohomolo...
AbstractLet K be a p-adic field, R the valuation ring of K, and P the maximal ideal of R. Let Y⊆R2 b...
AbstractWe give bounds for exponential sums associated to functions on curves defined over Galois ri...
We introduce T-adic exponential sums associated to a Laurent polynomial f. They interpolate all clas...
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 20...
We extend some methods of bounding exponential sums of the type ∑n≤Ne²πiagn/p to deal with the case ...
Given a prime p and an integer d > 1, we give a numerical criterion to decide whether the ℓ-adic she...
AbstractIn this article, we consider the estimation of exponential sums along the points of the redu...
Let $\mathbb{F}_{q}$ be a finite field with characteristic $p$. A fundamental problem in number theo...
We develop a theory concerning the reconstruction of multivariate exponential sums first over arbitr...
One contribution of 8 to a Theo Murphy meeting issue ‘Number fields and function fields: coalescence...
The main theme of this thesis is the study of compatible systems of $\ell$-adic Galoi...
We prove the remaining part of the conjecture by Denef and Sperber [Denef, J. and Sperber, S., Expon...
Abstract. Let C be a smooth curve over O/plO, O being the valuation ring of an unramified extension ...
AbstractIn this paper we compute geometric monodromy groups of additive exponential sums over BbbAn....
We deduce Katz's theorems for $(A,B)$-exponential sums over finite fields using $\ell$-adic cohomolo...
AbstractLet K be a p-adic field, R the valuation ring of K, and P the maximal ideal of R. Let Y⊆R2 b...
AbstractWe give bounds for exponential sums associated to functions on curves defined over Galois ri...
We introduce T-adic exponential sums associated to a Laurent polynomial f. They interpolate all clas...
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 20...
We extend some methods of bounding exponential sums of the type ∑n≤Ne²πiagn/p to deal with the case ...
Given a prime p and an integer d > 1, we give a numerical criterion to decide whether the ℓ-adic she...
AbstractIn this article, we consider the estimation of exponential sums along the points of the redu...
Let $\mathbb{F}_{q}$ be a finite field with characteristic $p$. A fundamental problem in number theo...
We develop a theory concerning the reconstruction of multivariate exponential sums first over arbitr...
One contribution of 8 to a Theo Murphy meeting issue ‘Number fields and function fields: coalescence...
The main theme of this thesis is the study of compatible systems of $\ell$-adic Galoi...
We prove the remaining part of the conjecture by Denef and Sperber [Denef, J. and Sperber, S., Expon...
Abstract. Let C be a smooth curve over O/plO, O being the valuation ring of an unramified extension ...
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