We study subgraphs of Paley graphs of prime order p induced on the sets of vertices
extending a given independent set of size a to a larger independent set. Using a sufficient …

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a
certain power condition and use it to prove several generalizations of Igusa's conjecture on …

In this note, we focus on how many arithmetic progressions we have in certain subsets of
finite fields. For this purpose, we consider the sets S p={t 2: t∈ F p} and C p={t 3: t∈ F p} …

Given two irreducible conics $ C $ and $ D $ over a finite field $\mathbb {F} _q $ with $ q $
odd, we show that there are $ q^ 2/4+ O (q^{3/2}) $ points $ P $ in $\mathbb {P}^ 2 (\mathbb …

We formulate a general problem: Given projective schemes YY and XX over a global field K
and a K‐morphism η from YY to XX of finite degree, how many points in X (K) X(K) of height …

We obtain upper bounds for the number of monic irreducible polynomials over $\mathbb Z $
of a fixed degree $ n $ and a growing height $ H $ for which the field generated by one of its …

Let $ X\subset\mathbf {P} _ {\mathbf {Q}}^{n-1} $ be a cubic hypersurface cut out by the
vanishing of a non-degenerate rational cubic form in $ n $ variables. Let $ N (X, B) $ denote …

We prove a stratification result for certain families of n-dimensional (complete algebraic)
multiplicative character sums. The character sums we consider are sums of products of r …

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DISTRIBUTION OF POLYNOMIAL DISCRIMINANTS MODULO A PRIME 1. Introduction 1.1.
Motivation. For an integer n and a prime power q, w Page 1 DISTRIBUTION OF POLYNOMIAL …