# Ernest S. Croot III

#22,944

Most Influential Person Now

American mathematician

## Ernest S. Croot III's AcademicInfluence.com Rankings

Ernest S. Croot IIImathematics Degrees

Mathematics

#1329

World Rank

#2221

Historical Rank

#549

USA Rank

Measure Theory

#5378

World Rank

#6376

Historical Rank

#1508

USA Rank

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Mathematics

## Ernest S. Croot III's Degrees

- PhD Mathematics University of California, Berkeley
- Masters Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley

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## Why Is Ernest S. Croot III Influential?

(Suggest an Edit or Addition)According to Wikipedia, Ernest S. Croot III is a mathematician and professor at the School of Mathematics, Georgia Institute of Technology. He is known for his solution of the Erdős–Graham conjecture, and for contributing to the solution of the cap set problem.

## Ernest S. Croot III's Published Works

### Published Works

- Progression-free sets in Z_4^n are exponentially small (2016) (156)
- A Probabilistic Technique for Finding Almost-Periods of Convolutions (2010) (101)
- Open problems in additive combinatorics (2007) (54)
- Progression-free sets in $\mathbb Z_4^n$ are exponentially small (2017) (52)
- Arithmetic Progressions in Sumsets and Lp-Almost-Periodicity (2011) (36)
- h-Fold Sums from a Set with Few Products (2009) (28)
- Arithmetic progressions in sparse sumsets (2007) (27)
- On a coloring conjecture about unit fractions (2003) (18)
- The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit (2004) (17)
- On the Distribution of Eigenvalues of Grand Canonical Density Matrices (2002) (15)
- On sharp transitions in making squares (2008) (13)
- On some questions of Erdős and Graham about Egyptian fractions (1999) (12)
- Sums of the Form 1/x (2004) (11)
- SMOOTH NUMBERS IN SHORT INTERVALS (2007) (11)
- A new proof of Roth’s theorem on arithmetic progressions (2008) (10)
- Running Time Predictions for Factoring Algorithms (2008) (9)
- Complexity of inverting the Euler function (2004) (9)
- On a Certain Generalization of the Balog-Szemerédi-Gowers Theorem (2008) (9)
- Binary Egyptian Fractions (2000) (9)
- The abc conjecture and correctly rounded reciprocal square roots (2004) (8)
- On unit fractions with denominators in short intervals (1999) (8)
- On the oscillations of multiplicative functions taking values ±1 (2002) (6)
- Few products, many h-fold sums (2014) (6)
- On a combinatorial method for counting smooth numbers in sets of integers (2003) (6)
- Long arithmetic progressions in critical sets (2004) (5)
- On Sumsets and Spectral Gaps (2007) (5)
- On Rich Lines in Grids (2008) (5)
- Polynomials and Primes in Generalized Arithmetic Progressions (2013) (5)
- Sets of rich lines in general position (2013) (4)
- A Purely Combinatorial Approach to Simultaneous Polynomial Recurrence Modulo 1 (2013) (4)
- Some Properties of Lower Level-Sets of Convolutions (2011) (3)
- On sums and products in ℂ[x] (2010) (3)
- On the Decay of the Fourier Transform and Three Term Arithmetic Progressions (2006) (3)
- A Structure Theorem for Positive Density Sets Having the Minimal Number of 3-term Arithmetic Progressions (2003) (2)
- On sums and products in C[x] (2008) (2)
- k-Term Arithmetic Progressions in Very Sparse Sumsets (2008) (1)
- Unit Fractions and the Class Number of a Cyclotomic Field (2002) (1)
- Reciprocal Power Sums Modulo a Prime (2004) (1)
- Research Problems in Arithmetic Combinatorics (1)
- Subsets of F_p^n without three term arithmetic progressions have several large Fourier coefficients (2007) (1)
- On non-intersecting arithmetic progressions (2002) (1)
- Notes on the chi-squared distribution Ernie Croot (2008) (1)
- Notes on Szemeredi’s Regularity Lemma (1)
- Sum-Product Inequalities with Perturbation (2009) (1)
- The structure of critical sets for F_p arithmetic progressions (2007) (1)
- ARITHMETIC PROGRESSIONS IN SPARSE SUMSETS Dedicated to Ron Graham on the occasion of his 70 th birthday (2005) (0)
- On a Class of Sums with Unexpectedly High Cancellation, and its Applications (2019) (0)
- 2 M ar 2 00 4 Reciprocal Power Sums Modulo a Prime (2008) (0)
- Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version) (2013) (0)
- On a conjecture of Graham on the p-divisibility of central binomial coefficients (2022) (0)
- An Outline of the Thue-Siegel Theorem Ernie Croot May (0)
- Sum-product inequalities with perturbation Dedicated to Mel Nathanson (2009) (0)
- k-term Arithmetic Progressions in Sumsets (2004) (0)
- Notes 2 for Honors Probability and Statistics (2010) (0)
- Prime Graph and Its Structures (2023) (0)
- A combinatorial method for developing Lucas sequence identities (2008) (0)
- Research Statement (2008) (0)
- Order-Preserving Freiman Isomorphisms (2014) (0)
- An application of linear programming duality to discrete Fourier analysis and additive problems (2007) (0)
- Group Actions (2021) (0)
- k-fold sums from a set with few products Dedicated to the memory of Gyorgy Elekes (2009) (0)
- New Applications of the Polynomial Method to Problems in Combinatorics (2016) (0)
- An Exposition of the Balog-Szemerédi Theorem Ernie Croot (0)
- Some problems in additive combinatorics & analytic number theory (2011) (0)
- Memory Efficient Arithmetic (2003) (0)
- On the Structure of Sets with Few Three-Term Arithmetic Progressions (2006) (0)
- Sums of the Form 1/x_1^k + ... + 1/x_n^k Modulo a Prime (2004) (0)
- Arithmetic structures in smooth subsets of F_p (2007) (0)
- A PROBABILISTIC TECHNIQUE FOR FINDING ALMOST-PERIODS IN ADDITIVE COMBINATORICS (2010) (0)
- eb 2 00 9 On sums and products in C [ x ] (0)
- A ug 2 00 2 On the Oscillations of Multiplicative Functions Taking Values ± (1990) (0)

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