Victor Z. Guo

activity

20152026

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math.NT2015

Quadratic nonresidues below the Burgess bound

William D. Banks, Victor Z. Guo

For any odd prime number $p$ , let $(\cdot ∣ p)$ be the Legendre symbol, and let $n_{1} (p) < n_{2} (p) < \dots$ be the sequence of positive nonresidues modulo $p$ , i.e., $(n_{k} ∣ p) = - 1$ for each…

math.NT2015

Some arithmetic properties of numbers of the form $⌊ p^{c} ⌋$

William D. Banks, Victor Z. Guo, Igor E. Shparlinski

Let $P^{c} = (⌊ p^{c} ⌋)_{p \in P} (c > 1, c \neq \in N),$ where $P$ is the set of prime numbers, and $⌊ \cdot ⌋$ is the…

math.NT2015

Piatetski-Shapiro Primes in a Beatty Sequence

Victor Z. Guo

Let $α, β$ be real numbers such that $α > 1$ is irrational and of finite type, and let $c$ be a real number in the range $1 < c < \frac{14}{13}$ . In this paper, it is shown that there are…

Quadratic nonresidues below the Burgess bound

Some arithmetic properties of numbers of the form ⌊pc⌋

Piatetski-Shapiro Primes in a Beatty Sequence

Some arithmetic properties of numbers of the form $⌊ p^{c} ⌋$