W. Banks

activity

20042026

most citedDensity of non-residues in Burgess-type intervals and applications

19 citations · 99 across the 36 of their papers we have counts for

collaborators

Showing 2015 · math.NTShow all

5 papers · 2 filters

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

Zeta functions and asymptotic additive bases with some unusual sets of primes

William D. Banks

Fix $δ \in (0, 1]$ , $σ_{0} \in [0, 1)$ and a real-valued function $ε (x)$ for which $lim sup_{x \to \infty} ε (x) \leq 0$ . For every set of primes $P$ whose countin…

math.NT2015★ 6 cited

Every natural number is the sum of forty-nine palindromes

William D. Banks

It is shown that the set of decimal palindromes is an additive basis for the natural numbers. Specifically, we prove that every natural number can be expressed as the sum of forty-…

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

Carmichael numbers and the sieve

William D. Banks, Tristan Freiberg

Using the sieve, we show that there are infinitely many Carmichael numbers whose prime factors all have the form $p = 1 + a^{2} + b^{2}$ with $a, b \in Z$ .

Quadratic nonresidues below the Burgess bound

Zeta functions and asymptotic additive bases with some unusual sets of primes

Every natural number is the sum of forty-nine palindromes

Some arithmetic properties of numbers of the form ⌊pc⌋

Carmichael numbers and the sieve

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