Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • LOG-SINE EVALUATIONS OF MAHLER MEASURES

  • Part of
  • JONATHAN M. BORWEIN, ARMIN STRAUB
  • Journal:
    Journal of the Australian Mathematical Society / Volume 92 / Issue 1 / February 2012
    Published online by Cambridge University Press:
    15 June 2012, pp. 15-36
    Print publication:
    February 2012
    • Article
      • You have access
    • PDF
    • Export citation

  • We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.

  • Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

  • Douglas Bowman, David M. Bradley
  • Journal:
    Compositio Mathematica / Volume 139 / Issue 1 / October 2003
    Published online by Cambridge University Press:
    04 December 2007, pp. 85-100
    Print publication:
    October 2003
    • Article
      • You have access
    • PDF
    • Export citation

  • We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.