[NEMO-devel] Expanding Nemo as a wrapper Arb

Kevin O'Bryant Kevin.OBryant at csi.cuny.edu
Fri Sep 27 06:20:10 AEST 2019

I'm a combinatorialist making forays into explicit analytic number theory. I've always used Mathematica, but for various reasons I'm trying to switch, to the extent possible, to Julia. As such, I'd like to use Nemo, and in particular am attracted to Nemo as a "wrapper" for Arb. I do have Julia & Nemo installed, and the examples given in the Nemo documentation work (including using Arbs) as advertised.

I think I could extrapolate how to link to together the documentation of Arb, Nemo, and Julia, as it impacts the first goals I've set for my switch, if only I had a code snippet that would use interval arithmetic to give rigorous upper and lower bounds on the integral of L'(sigma+10.2 i, chi) / L(sigma+10.2 i, chi) as sigma goes from 1/2 to 3/2, with chi iterating over the characters modulo 5.

That would cover a few things I'm uncertain about, but need to do repeatedly: rigorous integrals, complex Arbs, L-functions and their derivatives, looping over characters. According to Mathematica's nonrigorous computation, the values are
{-0.443999 + 0.1765 i, -0.718527 - 0.30044 i, 0.264691 - 0.982218 i, -0.130411 - 0.184415 i}.

Apologies (and appreciation in advance for your help) for asking you to do my coding.

Fredrik Johansson (personal communication) suggested that this would require more interface code for Dirichlet characters and acb_dirichlet_l_jet since these functions haven't been wrapped in Nemo yet.

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