×

Hypergeometric \(L\)-functions in average polynomial time. (English) Zbl 1472.11316

Galbraith, Steven D. (ed.), ANTS XIV. Proceedings of the fourteenth algorithmic number theory symposium, Auckland, New Zealand, virtual event, June 29 – July 4, 2020. Berkeley, CA: Mathematical Sciences Publishers (MSP). Open Book Ser. 4, 143-159 (2020).
Summary: We describe an algorithm for computing, for all primes \(p\le X\), the mod-\(p\) reduction of the trace of Frobenius at \(p\) of a fixed hypergeometric motive in time quasilinear in \(X\). This combines the Beukers-Cohen-Mellit trace formula with average polynomial time techniques by D. Harvey et al. [LMS J. Comput. Math. 19A, 220–234 (2016; Zbl 1404.11143)].
For the entire collection see [Zbl 1452.11005].

MSC:

11Y16 Number-theoretic algorithms; complexity
33C20 Generalized hypergeometric series, \({}_pF_q\)
11G09 Drinfel’d modules; higher-dimensional motives, etc.
11M38 Zeta and \(L\)-functions in characteristic \(p\)
11T24 Other character sums and Gauss sums

Citations:

Zbl 1404.11143
PDFBibTeX XMLCite
Full Text: DOI arXiv