Opened 8 years ago

Closed 6 years ago

#16782 closed defect (fixed)

Riemann and Hurwitz Zeta functions for complex and real intervals

Reported by: cheuberg Owned by:
Priority: major Milestone: sage-7.1
Component: numerical Keywords: complex interval, CIF, Riemann zeta function
Cc: dkrenn, skropf, kcrisman, robertwb, mmezzarobba Merged in:
Authors: Clemens Heuberger Reviewers: Fredrik Johansson
Report Upstream: N/A Work issues:
Branch: 7a590fb (Commits, GitHub, GitLab) Commit: 7a590fba8e206b24b4a74f8c10dca4db31ca7eb4
Dependencies: Stopgaps:

Status badges

Description (last modified by cheuberg) 

    sage: zeta(RIF(3))
    1.20205690315959
    sage: _.parent()
    Complex Field with 53 bits of precision
    sage: zeta(CIF(2, 3))
    0.798021985146276 - 0.113744308052939*I
    sage: _.parent()
    Complex Field with 53 bits of precision

(see ticket:19993#comment:10).

Fix this by conversion to arb, computation of zeta there, and conversion back. (mpfi does not seem to have a zeta function).

Change History (14)

comment:1 Changed 8 years ago by cheuberg

I do have a TeX file containing additional (boring) computations documenting parts of the code, but I am not sure where to put it, see my post on ​sage-devel.

comment:2 Changed 8 years ago by git

  • Commit changed from 315df6e141e10ca352984fe206b59021c8e58e77 to a947cfcdf4467fd95e507f7128151c1a204e27ef

Branch pushed to git repo; I updated commit sha1. New commits:

​a947cfcTrac #16782: Fix trivial typo in docstring

comment:3 Changed 8 years ago by git

  • Commit changed from a947cfcdf4467fd95e507f7128151c1a204e27ef to 67bee310b1717021d29bf75bc1b3f20cbb3dee7b

Branch pushed to git repo; I updated commit sha1. New commits:

​67bee31Trac #16782: Fix function name in verbose output.

comment:4 follow-up: Changed 8 years ago by fredrik.johansson

Riemann zeta for complex intervals could also be implemented using the Arb library (#16747).

comment:5 Changed 8 years ago by git

  • Commit changed from 67bee310b1717021d29bf75bc1b3f20cbb3dee7b to 4608c670a1a803b8d6a5eacf8ef64d3669976bbb

Branch pushed to git repo; I updated commit sha1. New commits:

​4608c67Trac #16782: Add example and TODO concerning negative real values of s

comment:6 in reply to: ↑ 4 Changed 8 years ago by cheuberg

Replying to fredrik.johansson:

Riemann zeta for complex intervals could also be implemented using the Arb library (#16747).

Thank you for pointing that out; once #16747 is included and there are conversions between CIF and arb, that would certainly be the better option.

comment:7 Changed 8 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:8 Changed 8 years ago by cheuberg

  • Branch u/cheuberg/rings/zeta-CIF deleted
  • Commit 4608c670a1a803b8d6a5eacf8ef64d3669976bbb deleted

Deleted the branch as it was not the way to proceed.

comment:9 Changed 8 years ago by jdemeyer

  • Description modified (diff)

comment:10 Changed 6 years ago by cheuberg

  • Description modified (diff)
  • Milestone changed from sage-6.4 to sage-7.1
  • Summary changed from Riemann Zeta function for complex interval to Riemann Zeta function for complex and real intervals
  • Type changed from enhancement to defect

comment:11 Changed 6 years ago by cheuberg

  • Branch set to u/cheuberg/rifcif-zeta

comment:12 Changed 6 years ago by cheuberg

  • Cc mmezzarobba added
  • Commit set to 7a590fba8e206b24b4a74f8c10dca4db31ca7eb4
  • Status changed from new to needs_review
  • Summary changed from Riemann Zeta function for complex and real intervals to Riemann and Hurwitz Zeta functions for complex and real intervals

New commits:

​7a590fbTrac #16782: implement zeta function for RIF and CIF

comment:13 Changed 6 years ago by fredrik.johansson

  • Reviewers set to Fredrik Johansson
  • Status changed from needs_review to positive_review

This looks good to me.

comment:14 Changed 6 years ago by vbraun

  • Branch changed from u/cheuberg/rifcif-zeta to 7a590fba8e206b24b4a74f8c10dca4db31ca7eb4
  • Resolution set to fixed
  • Status changed from positive_review to closed
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