Author

Hamed Ebadi

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Preprint Oct 2026

Moments and Large Geometric Monodromy for Linearly Constrained Kloosterman Families

Let $q=p^a$ with $p$ prime, $\lambda\in\mathbb F_p^\times$, and $\psi_q=\psi\circ\mathrm{Tr}_{\mathbb F_q/\mathbb F_p}$ for a nontrivial additive character $\psi$ of $\mathbb F_p$. For $n\ge2$ we study $\Sigma_n(h)=\sum_{u\in(\mathbb F_q^\times)^n,\sum_i h_i u_i=-\lambda}\psi_q(\sum_i u_i^{-1})$. On $\mathbb G_m^n$ we...

Hamed Ebadi · 0 citations

Preprint Oct 2026

Cohomology of Linearly Constrained Kloosterman Families: Newton Polytopes, Weights, and Boundary Monodromy

Let $p$ be an odd prime, $\psi$ a nontrivial additive character of $\mathbb F_p$, $\psi_q=\psi\circ\mathrm{Tr}_{\mathbb F_q/\mathbb F_p}$ and $\lambda\in\mathbb F_p^\times$. For $h\in(\mathbb F_q^\times)^n$ let $\Sigma_n(h)$ be the sum of $\psi_q(u_1^{-1}+\cdots+u_n^{-1})$ over $u\in(\mathbb F_q^\times)^n$ with $h_1u_1...

Hamed Ebadi · 0 citations

Preprint Oct 2026

Moments and Large Geometric Monodromy for Linearly Constrained Kloosterman Families

We determine the connected geometric monodromy of the top-weight sheaves attached to linearly constrained Kloosterman families in every dimension n>= 4 and every characteristic p>max(2,n). The quantitative input is a fourth-moment identity whose auxiliary geometry depends on the moment degree rather than on the ambient...

Hamed Ebadi · 0 citations