Shuhong Gao

activity

20002026

most citedFinite field elements of high order arising from modular curves

14 citations · 44 across the 12 of their papers we have counts for

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4 papers · 1 filter

math.NT2024

On binomial Weil sums and an application

Kaimin Cheng, Shuhong Gao

Let $p$ be a prime, and $N$ be a positive integer not divisible by $p$ . Denote by $ord_{N} (p)$ the multiplicative order of $p$ modulo $N$ . Let $F_{q}$ represent the fini…

math.NT2017★ 9 cited

Counting Roots of Polynomials Over Prime Power Rings

Qi Cheng, Shuhong Gao, J. Maurice Rojas +1

Suppose $p$ is a prime, $t$ is a positive integer, and $f \in Z [x]$ is a univariate polynomial of degree $d$ with coefficients of absolute value $< p^{t}$ . We show that f…

math.NT2014★ 2 cited

Sparse Univariate Polynomials with Many Roots Over Finite Fields

Qi Cheng, Shuhong Gao, J. Maurice Rojas +1

Suppose $q$ is a prime power and $f \in F_{q} [x]$ is a univariate polynomial with exactly $t$ monomial terms and degree $< q - 1$ . To establish a finite field analogue of Descart…

math.NT2012★ 14 cited

Finite field elements of high order arising from modular curves

Jessica F. Burkhart, Neil J. Calkin, Shuhong Gao +6

In this paper, we recursively construct explicit elements of provably high order in finite fields. We do this using the recursive formulas developed by Elkies to describe explicit…