Vol. 1, No. 1, 2007

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Functional equations for Mahler measures of genus-one curves

Matilde N. Lalin and Mathew D. Rogers

Vol. 1 (2007), No. 1, 87–117
Abstract

In this paper we will establish functional equations for Mahler measures of families of genus-one two-variable polynomials. These families were previously studied by Beauville, and their Mahler measures were considered by Boyd, Rodriguez Villegas, Bertin, Zagier, and Stienstra. Our functional equations allow us to prove identities between Mahler measures that were conjectured by Boyd. As a corollary, we also establish some new transformations for hypergeometric functions.

Keywords
Mahler measure, L-functions, Bloch–Beilinson conjectures, Kronecker–Eisenstein series, elliptic regulator, hypergeometric identities, modular equations
Mathematical Subject Classification 2000
Primary: 11R09
Secondary: 11F66, 19F27, 33C05, 33C20
Milestones
Received: 9 February 2007
Accepted: 7 July 2007
Published: 1 February 2007
Authors
Matilde N. Lalin
Department of Mathematical and Statistical Sciences
632 Central Academic Building
University of Alberta
Edmonton, AB T6G 2G1
Canada
http://www.math.ubc.ca/~mlalin
Mathew D. Rogers
Department of Mathematics
University of British Columbia
Vancouver, BC V6T 1Z2
Canada
http://www.math.ubc.ca/~matrogers