Introduces δ(G,H) for finite abelian quotients, proves δ(G,H) ≥ 2|G/H| - m(G,H) sharp for cyclic cases, and conjectures δ=(2p-1)² for the (Z/p²Z)² case with lower bound 3p²-p-1.
On the size of Kakeya sets in finite fields
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abstract
A Kakeya set is a subset of F^n, where F is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least C_n * q^n, where C_n depends only on n. This improves the previously best lower bound for general n of ~q^{4n/7}.
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math.NT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Transversal Difference Numbers in Finite Abelian Quotients
Introduces δ(G,H) for finite abelian quotients, proves δ(G,H) ≥ 2|G/H| - m(G,H) sharp for cyclic cases, and conjectures δ=(2p-1)² for the (Z/p²Z)² case with lower bound 3p²-p-1.