Author

Zhi Yao

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Preprint Aug 2026

Five-Term and Higher Congruences Involving Arbitrary Sets and Short Intervals Modulo a Prime

We obtain asymptotic formulas for additive congruences \[ \sum_{i=1}^r m_i x_i^{-s}\equiv \lambda \pmod p, \] where the $m_i$ range over arbitrary subsets of $\mathbb F_p^\ast$ and the $x_i$ over shifted intervals. For five terms, in the balanced case of common cardinality $N$, the asymptotic holds uniformly in...

Zhi Yao · 0 citations

Preprint Aug 2026

Quadratic Expansion over Prime Fields via Centered Collisions and Popular-Sum Amplification

Let $p$ be an odd prime, let $\varnothing\neq A\subseteq\mathbb F_p$ have cardinality $N$, and let $f\in\mathbb F_p[x,y]$ be a non-degenerate quadratic polynomial. Writing $S=|A+A|$ and $M=|f(A,A)|$, we prove the full-range trade-off $S^8M^6\gtrsim N^{17}(1+N^3/p^2)^{-3}$. Consequently, $\max\{|A+A|,|f(A,A)|\}\gtrsim \...

Zhi Yao · 0 citations