2011/11/29 by Byugheup Jun, Jungyun Lee, Jun, Byugheup +1
Mathematics · #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1111.6717
openalex publication_date 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the special values of partial zeta function at s=0 for family of real quadratic fields Kn and ray class ideals \fbn such that \fbn-1 = [1,δ(n)] where the continued fraction expansion of δ(n) is purely periodic and each terms are polynomial in n of bounded degree d. With an additional assumptions, we prove that the special values of partial zeta function at s=0 behaves as quasi-polynomial. We apply this to obtain that the special values the Hecke's L-functions at s=0 for a family of for a Dirichlet character χ behave as quasi-polynomial as well. We compute out explicitly the coefficients of the quasi-polynomials. Two examples satisfying the condition are presented and for these families the special values of the partial zeta functions at s=0.