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arXiv · 1907.08389

Mahler measures of a family of non-tempered polynomials and Boyd's conjectures

Yotsanan Meemark·Detchat Samart
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Abstract

We prove an identity relating Mahler measures of a certain family of non-tempered polynomials to those of tempered polynomials. Evaluations of Mahler measures of some polynomials in the first family are also given in terms of special values of $L$-functions and logarithms. Finally, we prove Boyd's conjectures for conductor $30$ elliptic curves using our new identity, Brunault-Mellit-Zudilin's formula and additional functional identities for Mahler measures.

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Yotsanan Meemark, Detchat Samart. 2019-07-19. Mahler measures of a family of non-tempered polynomials and Boyd's conjectures. https://doi.org/10.1007/s40687-019-0200-6

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