32 citations · 43 across the 5 of their papers we have counts for
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math.NT2009★ 6 cited
Fourier analysis and expanding phenomena in finite fields
Derrick Hart, Liangpan Li, Chun-Yen Shen
In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi, Vinh and Vu using spectral grap…
math.NT2007★ 32 cited
Garaev's Inequality in finite fields not of prime order
Nets Hawk Katz, Chun-Yen Shen
We prove a version of Garaev's sum product theorem in the set of finite fields with non-prime order. Because of the presence of subfields, this seems to require some hypotheses on…
math.NT2007★ 2 cited
A Slight Improvement to Garaev's Sum Product Estimate
Nets Hawk Katz, Chun-Yen Shen
We slightly improve Garaev's recent sum-product estimate largely by using Plunneke's inequality a little more efficiently. We improve the exponent from 15/14 to 14/13.