New growth bounds for set products in the Heisenberg and affine groups over prime fields, plus an application to Freiman's isomorphism in nonabelian groups.
Modular hyperbolas and bilinear forms of Kloosterman sums
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abstract
In this paper we study incidences for hyperbolas in $\mathbf{F}_p$ and show how linear sum--product methods work for such curves. As an application we give a purely combinatorial proof of a nontrivial upper bound for bilinear forms of Kloosterman sums.
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math.CO 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Some remarks on products of sets in the Heisenberg group and in the affine group
New growth bounds for set products in the Heisenberg and affine groups over prime fields, plus an application to Freiman's isomorphism in nonabelian groups.