3 papers
math.NT2026
Shifted dihedral isogeny quotients and the classification of exceptional rational functions of degree five
Zhichao Tang, Xiang Fan
We give a complete classification, up to -Möbius equivalence, of exceptional rational functions of degree five over every finite field. The classification gives explicit normal…
quant-ph2025
Revisiting finite Abelian hidden subgroup problem and its distributed exact quantum algorithm
Ziyuan Dong, Xiang Fan, Tengxun Zhong +1
We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we p…
quant-ph2025
Probabilistic Bounds on the Number of Elements to Generate Finite Nilpotent Groups and Their Applications
Ziyuan Dong, Xiang Fan, Tengxun Zhong +1
This work establishes a new probabilistic bound on the number of elements to generate finite nilpotent groups. Let denote the probability that random elements generat…