3 papers
math.NT2025
Comparison of canonical periods under base change
Qingshen Lv, Bingyong Xie
In this paper we prove the canonical period of a Hilbert modular form with respect to the base change of a real quadratic extension differs from the square of its own canonical per…
math.CO2024
Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems
Bing Xie, Yigeng Zhao, Yongqiang Zhao
In this paper, we apply the combinatorial results on counting permutations with fixed pinnacle and vale sets to evaluate the special values of the spectral zeta functions of Sturm-…
math.NT2024
Hilbert modular forms and class numbers
Qinyun Tan, Bingyong Xie
In 1975, Goldfeld gave an effective solution to Gauss's conjecture on the class numbers of imaginary quadratic fields. In this paper, we generalize Goldfeld's theorem to the settin…