Opened 5 years ago

Closed 5 years ago

#23780 closed enhancement (fixed)

Modify p-adic Gauss sum to allow working directly in Q_p

Reported by: kedlaya Owned by:
Priority: major Milestone: sage-8.1
Component: padics Keywords: Gauss sums, Gross-Koblitz formula
Cc: Merged in:
Authors: Kiran Kedlaya Reviewers: David Roe, Frédéric Chapoton
Report Upstream: N/A Work issues:
Branch: 45da482 (Commits, GitHub, GitLab) Commit: 45da48281b575794afe1e83f2378f80418c5c7d8
Dependencies: Stopgaps:

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Description

The Gross-Koblitz formula for p-adic computation of Gauss sums was implemented in #23456. The formula involves working in the ramified extension of Q_p generated by an element pi for which pi^(p-1) == -p; however, the formula actually is written as a power of pi times an element of Z_p, and for some applications (e.g., hypergeometric motives; see #23671) it would be helpful to be able to access the unramified factor without going through the extension ring (for efficiency when p is large). That is, one should have the option to request the output in the form (e, z) where e is a nonnegative integer, z is an element of Z_p, and the real answer is pi^e*z for pi as above. And in this case, the extension field should not be formed at all.

Change History (13)

comment:1 Changed 5 years ago by kedlaya

  • Branch set to u/kedlaya/modify_p_adic_gauss_sum_to_allow_working_directly_in_q_p

comment:2 Changed 5 years ago by git

  • Commit set to 50cd8bf9f3ea296f3894a550f91cc99e33cdeb98

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

50cd8bfFixed typo in doctest

comment:3 Changed 5 years ago by kedlaya

  • Status changed from new to needs_review

Commit added, with a doctest to match. I also fixed the mathematical issue with the docstring reported in #23671.

This should be an easy review, except possibly for formatting issues.

comment:4 Changed 5 years ago by roed

  • Reviewers set to David Roe

Looks good to me; positive review once tests pass.

comment:5 Changed 5 years ago by git

  • Commit changed from 50cd8bf9f3ea296f3894a550f91cc99e33cdeb98 to 6cc03a1bc2f4e116854e9243d229b7998ab5789a

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

6cc03a1Correct docstring formatting, handling of r=0 case

comment:6 Changed 5 years ago by kedlaya

Fixed docstring formatting in my mathematical correction; and forced the answer to be cast into the p-adic ring even when r=0 (otherwise errors may result down the line).

comment:7 Changed 5 years ago by chapoton

does not apply on the latest beta, needs rebase

comment:8 Changed 5 years ago by git

  • Commit changed from 6cc03a1bc2f4e116854e9243d229b7998ab5789a to ef1626f70212fd236a888e874a644fcb8cb1f4ea

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

ef1626fMerge branch 'develop' into t/23780/modify_p_adic_gauss_sum_to_allow_working_directly_in_q_p

comment:9 Changed 5 years ago by kedlaya

Sorry, that should be fixed now.

comment:10 Changed 5 years ago by roed

  • Authors set to Kiran Kedlaya

Adding author for patchbot.

comment:11 Changed 5 years ago by chapoton

  • Branch changed from u/kedlaya/modify_p_adic_gauss_sum_to_allow_working_directly_in_q_p to public/23780
  • Commit changed from ef1626f70212fd236a888e874a644fcb8cb1f4ea to 45da48281b575794afe1e83f2378f80418c5c7d8

trying to make the doc build.


New commits:

45da482trac 23780 some doc formatting details

comment:12 Changed 5 years ago by chapoton

  • Reviewers changed from David Roe to David Roe, Frédéric Chapoton
  • Status changed from needs_review to positive_review

ok, let it be.

comment:13 Changed 5 years ago by vbraun

  • Branch changed from public/23780 to 45da48281b575794afe1e83f2378f80418c5c7d8
  • Resolution set to fixed
  • Status changed from positive_review to closed
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