We investigate the sums $(1/\sqrt {H})\sum_ {X< n\leq X+ H}\chi (n) $, where $\chi $ is a fixed
non-principal Dirichlet character modulo a prime $ q $, and $0\leq X\leq q-1$ is uniformly …

We show that under certain general conditions, short sums of ℓ-adic trace functions over
finite fields follow a normal distribution asymptotically when the origin varies, generalising …

It is known that under the Generalized Riemann Hypothesis, the smallest quadratic non-
residue modulo a prime is less than or equal to. In ranges slightly larger, of size with, we …

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 …

To illustrate vertical and horizontal equidistributions of Kloosterman sums, we prove two
relevant central limit theorems by some analytic and combinatorial properties of Chebyshev …

Assuming the generalized Lindelöf hypothesis (GLH), a weak version of the generalized
Ramanujan conjecture and a Rankin–Selberg type partial sum estimate, we establish the …

Let $ p $ be a prime number, $ C $ be any absolutely irreducible affine plane curve over
$\mathbb {F} _p $, and $ g, f\in\mathbb {F} _p (x, y) $ be rational functions. We continue the …

The distribution of quadratic residues and non-residues in the Goldwasser–Micali type of
cryptosystem. II Page 1 DOI 10.1515/jmc-2014-0004 J. Math. Cryptol. 2015; 9 (2):115–137 …

We consider $\ell $-adic trace functions over finite fields taking values in cyclotomic integers,
such as characters and exponential sums. Through ideas of Deligne and Katz, we explore …

Let p be a large prime, ℓ⩾ 2 be a positive integer, m⩾ 2 be an integer relatively prime to ℓ
and P (x)∈ F p [x] be a polynomial which is not a complete ℓ′-th power for any ℓ′ for …