Computing zeta functions for ordinary formal groups over finite fields

✍ Scribed by Takakazu Satoh; Yuichiro Taguchi

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 181 KB
• Volume: 130
• Category: Article
• ISSN: 0166-218X
• DOI: 10.1016/s0166-218x(02)00589-9

✦ Synopsis

We describe an algorithm to compute the one-dimensional part of the zeta function ZG of an ordinary formal group law G of ÿnite dimension d over a ÿnite ÿeld of p N elements and evaluate its time computational complexity. Assume G is given as d formal power series in 2d variables. Our algorithm computes ZG mod p t with O(d 2 p (t-1)(2d+3) N 2 (log p) 2 ) bit operations.