Gaussian phenomena for small quadratic residues and non-residues

Basak, Debmalya; Nath, Kunjakanan; Zaharescu, Alexandru

doi:10.1090/tran/8853

Gaussian phenomena for small quadratic residues and non-residues
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by Debmalya Basak, Kunjakanan Nath and Alexandru Zaharescu HTML | PDF

Trans. Amer. Math. Soc. 376 (2023), 3695-3724 Request permission

Abstract:

Assuming the Generalized Riemann Hypothesis, it is known that the smallest quadratic non-residue modulo a prime $p$ is less than or equal to $(\log p)^2$. Our aim in this paper is to establish the distribution of quadratic non-residues in even smaller intervals of size $(\log p)^A$ with $A >1$, for almost all primes $p$.

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