Ernie Croot

524 total citations
17 papers, 151 citations indexed

About

Ernie Croot is a scholar working on Discrete Mathematics and Combinatorics, Geometry and Topology and Algebra and Number Theory. According to data from OpenAlex, Ernie Croot has authored 17 papers receiving a total of 151 indexed citations (citations by other indexed papers that have themselves been cited), including 13 papers in Discrete Mathematics and Combinatorics, 9 papers in Geometry and Topology and 9 papers in Algebra and Number Theory. Recurrent topics in Ernie Croot's work include Limits and Structures in Graph Theory (13 papers), Analytic Number Theory Research (9 papers) and Advanced Topology and Set Theory (7 papers). Ernie Croot is often cited by papers focused on Limits and Structures in Graph Theory (13 papers), Analytic Number Theory Research (9 papers) and Advanced Topology and Set Theory (7 papers). Ernie Croot collaborates with scholars based in United States, Canada and United Kingdom. Ernie Croot's co-authors include Vsevolod F. Lev, Derrick Hart, Tomasz Schoen, Ren‐Cang Li, Imre Z. Ruzsa, Izabella Łaba, Hui June Zhu, Andrew Granville, Prasad Tetali and Robin Pemantle and has published in prestigious journals such as Mathematics of Computation, Annals of Mathematics and Theoretical Computer Science.

In The Last Decade

Ernie Croot

17 papers receiving 133 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Ernie Croot United States 6 100 69 55 40 31 17 151
Tom Sanders United Kingdom 9 143 1.4× 75 1.1× 69 1.3× 48 1.2× 35 1.1× 24 183
Kevin O’Bryant United States 6 70 0.7× 54 0.8× 35 0.6× 45 1.1× 43 1.4× 17 141
Yufei Zhao United States 9 161 1.6× 126 1.8× 111 2.0× 49 1.2× 26 0.8× 47 235
James Pommersheim United States 8 80 0.8× 56 0.8× 107 1.9× 73 1.8× 10 0.3× 24 180
Apoorva Khare United States 7 28 0.3× 48 0.7× 59 1.1× 36 0.9× 11 0.4× 31 120
Lê Anh Vinh Vietnam 7 155 1.6× 32 0.5× 63 1.1× 54 1.4× 37 1.2× 46 191
Sukumar Das Adhikari India 9 120 1.2× 66 1.0× 70 1.3× 105 2.6× 68 2.2× 39 223
Misha Rudnev United Kingdom 8 169 1.7× 40 0.6× 65 1.2× 60 1.5× 23 0.7× 19 205
Oliver Roche‐Newton Austria 7 98 1.0× 52 0.8× 32 0.6× 24 0.6× 7 0.2× 24 121
Robert Cowen United States 6 68 0.7× 191 2.8× 31 0.6× 14 0.3× 19 0.6× 23 220

Countries citing papers authored by Ernie Croot

Since Specialization
Citations

This map shows the geographic impact of Ernie Croot's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Ernie Croot with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Ernie Croot more than expected).

Fields of papers citing papers by Ernie Croot

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Ernie Croot. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Ernie Croot. The network helps show where Ernie Croot may publish in the future.

Co-authorship network of co-authors of Ernie Croot

This figure shows the co-authorship network connecting the top 25 collaborators of Ernie Croot. A scholar is included among the top collaborators of Ernie Croot based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Ernie Croot. Ernie Croot is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

17 of 17 papers shown
1.
Croot, Ernie, et al.. (2016). Progression-free sets in $\mathbb{Z}_4^n$ are exponentially small. Annals of Mathematics. 185(1). 57 indexed citations
2.
Croot, Ernie, et al.. (2013). Arithmetic Progressions in Sumsets and Lp-Almost-Periodicity. Combinatorics Probability Computing. 22(3). 351–365. 6 indexed citations
3.
Croot, Ernie, Andrew Granville, Robin Pemantle, & Prasad Tetali. (2012). On sharp transitions in making squares. Annals of Mathematics. 175(3). 1507–1550. 3 indexed citations
4.
Croot, Ernie, et al.. (2011). On a Certain Generalization of the Balog–Szemerédi–Gowers Theorem. SIAM Journal on Discrete Mathematics. 25(2). 685–694. 5 indexed citations
5.
Croot, Ernie & Derrick Hart. (2010). On sums and products in ℂ[x]. The Ramanujan Journal. 22(1). 33–54. 1 indexed citations
6.
Croot, Ernie & Derrick Hart. (2010). h-Fold Sums from a Set with Few Products. SIAM Journal on Discrete Mathematics. 24(2). 505–519. 11 indexed citations
7.
Croot, Ernie, et al.. (2010). A Probabilistic Technique for Finding Almost-Periods of Convolutions. Geometric and Functional Analysis. 20(6). 1367–1396. 38 indexed citations
8.
Croot, Ernie, et al.. (2010). On Rich Lines in Grids. Discrete & Computational Geometry. 43(4). 824–840. 1 indexed citations
9.
Croot, Ernie & Tomasz Schoen. (2008). On sumsets and spectral gaps. Acta Arithmetica. 136(1). 47–55. 2 indexed citations
10.
Croot, Ernie, et al.. (2008). A new proof of Roth’s theorem on arithmetic progressions. Proceedings of the American Mathematical Society. 137(3). 805–809. 2 indexed citations
11.
Croot, Ernie. (2008). The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit. Canadian Mathematical Bulletin. 51(1). 47–56. 5 indexed citations
12.
Croot, Ernie. (2007). On a combinatorial method for counting smooth numbers in sets of integers. Journal of Number Theory. 126(2). 237–253. 2 indexed citations
13.
Croot, Ernie. (2007). SMOOTH NUMBERS IN SHORT INTERVALS. International Journal of Number Theory. 3(1). 159–169. 5 indexed citations
14.
Croot, Ernie, et al.. (2006). Complexity of inverting the Euler function. Mathematics of Computation. 75(254). 983–996. 1 indexed citations
15.
Croot, Ernie. (2005). Long arithmetic progressions in critical sets. Journal of Combinatorial Theory Series A. 113(1). 53–66. 2 indexed citations
16.
Croot, Ernie, Imre Z. Ruzsa, & Tomasz Schoen. (2005). Arithmetic Progressions in Sparse Sumsets. Zenodo (CERN European Organization for Nuclear Research). 5 indexed citations
17.
Croot, Ernie, Ren‐Cang Li, & Hui June Zhu. (2004). The abc conjecture and correctly rounded reciprocal square roots. Theoretical Computer Science. 315(2-3). 405–417. 5 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

Explore authors with similar magnitude of impact

Breakdown of academic impact, for papers by Tom Sanders Breakdown of academic impact, for papers by Kevin O’Bryant Breakdown of academic impact, for papers by Yufei Zhao Breakdown of academic impact, for papers by James Pommersheim Breakdown of academic impact, for papers by Apoorva Khare Breakdown of academic impact, for papers by Lê Anh Vinh Breakdown of academic impact, for papers by Sukumar Das Adhikari Breakdown of academic impact, for papers by Misha Rudnev Breakdown of academic impact, for papers by Oliver Roche‐Newton Breakdown of academic impact, for papers by Robert Cowen
Rankless by CCL
2026