Mordell's exponential sum estimate revisited
By Jean Bourgain. 2005
114 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8f25d417c43762e696bbb7a25935a44891501080
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Peter Sarnak
- Harald Andrés Helfgott
- Jean Bourgain
- Alex Gamburd
- Igor E. Shparlinski
- Derrick Hart
- Doowon Koh
- Alex Iosevich
In Discrete Mathematics and Combinatorics
- Peter Sarnak
- Jean Bourgain
- Harald Andrés Helfgott
- Alex Gamburd
- P. P. Varj'u
- Igor E. Shparlinski
- Ilya D. Shkredov
- Derrick Hart
In Mathematical Physics
- Peter Sarnak
- Jean Bourgain
- Harald Andrés Helfgott
- Alex Gamburd
- Alex Kontorovich
- Igor E. Shparlinski
- P. P. Varj'u
- Alex Iosevich
Citations in the corpus
- Modular hyperbolas (2011, background): “We recall that several more bounds of exponential sums with sparse polynomials of large degree are also given in [30, 33, 59].”
- Open problems in additive combinatorics (2007, unknown): “We tried to include primarily those problems we came across in our research, or at least lying close to the area of our research interests.”
- Growth in SL_3(Z/pZ) (2008, methodology): “t theorem in (Z/pZ)n. We will prove a sum-product theorem of (Z/pZ)n. As a matter of fact, we shall use only the case n= 2; a theorem close to the one we need was already proven for n= 2 by Bourgain ([B]). However, [B] requires the assumption that |A| >pǫ. We cannot assume |A| >pǫin our applic”
- Affine linear sieve, expanders, and sum-product (2010, background): “Sum-product estimate in Zp for prime p [9] implies that for A ⊂ Zp satisfying |A| > p we have rA = Zp for r = r(τ ) (see Lemma 1 in [4]).”
- Pinned distance sets, k-simplices, Wolff’s exponent in finite fields and sum-product estimates (2009, background): “7 [4] J. Bourgain, A. Glibichuk, and S. Konyagin Estimates for the number of sums and products for exponentials sums in fields of prime order, Jour. of London Math.”