New bounds for Gauss sums derived from kth powers

By D. H. Brown, Sergei V. Konyagin. 2000

171 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/2c221dbf77808f57ad5b22afa4c442086090bf96

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Refined estimates concerning sumsets contained in the roots of unity (2019, methodology): “See [8] for another application of Stepanov’s method to an additive problem of roots of unity.”
New sum-product type estimates over finite fields (2014, methodology): “tiplicative subgroups in F. Bound (31) of the proposition below was proved in [29] in the case of the prime ﬁeld. The advantage of our more general result is the avoidance of using Stepanov’s method, [15] (even though the proof of Theorem 1 does use the polynomial method). We write F∗ for F \{0}. Pr”
Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order (2006, background): “Shparlinski [21] proved (4) under a weaker assumption |G| p, and this was further weakened to |G| p in [15] and to |G| p in [17].”
Growth and generation in $\mathrm{SL}_2(\mathbb{Z}/p \mathbb{Z})$ (2008, methodology): “Proof. The proofs of [ HBK , Lemma 5], [Ko, Lemma 5], and [Ko, Thm.”
On additive shifts of multiplicative subgroups (2011, methodology): “In the paper we extend the result of Garcia–Voloch and also similar theorems from [9], [13] for the case of several additive shifts.”
NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS (2017, unknown): “for A ⊂ R satisfying |A/A| ≪ |A|, and the fifth listed author’s and Vyugin’s lower bound [47] for small multiplicative subgroups Γ of Fp: |Γ− Γ| & |Γ|, which improves the lower bound of |Γ− Γ| ≫ |A|3/2 established by Heath-Brown and Konyagin [15].”
On the Divisibility of Fermat Quotients (2010, background): “Proof. We follow the arguments of the proof of Lemma 2 from [ 9 ].”