2006/08/30 by Victor Bautista-Ancona, Bautista-Ancona, Victor, Javier Diaz-Vargas +3
Computer Science · Mathematics · #11M38 #11M99 #Advanced Mathematical Identities #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Number Theory (math.NT) #math.NT #msc:11M38 #msc:11M99
paper · pdf · doi:10.48550/arxiv.math/0608755
Rocky Mountain Journal of Mathematics, to appear
arxiv created 2006/08/30 · openalex publication_date 2006/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Orders of vanishing of zeros of zeta functions have much arithmetic information encoded in them. For the absolute zeta function, Dinesh Thakur gave sufficient conditions for the order of vanishing of its zeros when the finite field has two elements. Such conditions consider only principal ideals. This result was generalized by Thakur and Diaz-Vargas. Now the conditions involve not only the principal ideals but all the classes of ideals, still in the field of two elements. In this work, we generalize these results to arbitrary finite fields, using similar proofs of Thakur and Diaz-Vargas.