Minimal Mahler Measure in Real Quadratic Fields

ABSTRACT

We investigate the upper and lower bounds on the minimal Mahler measure of an irrational number lying in a particular real quadratic field.

Keywords:

• Mahler measure
• Primary 11R06
• Secondary 11C08
• 11Y40

Funding

N. Donohoue and V. Pigno were supported in part by an I-Center Undergraduate Scholarship and an I-Center Graduate Scholarship, respectively, and C. Spencer was supported in part by NSA Young Investigator Grant #H98230-14-1-0164.

Acknowledgments

The authors thank Martin Widmer for pointing out the work of Ruppert and the referee for his careful comments, in particular the small examples with d ≡ 3 mod 4.