Regulator of modular units and Mahler measures. (English) Zbl 1386.11129

Summary: We present a proof of the formula, due to Mellit and Brunault, which evaluates an integral of the regulator of two modular units to the value of the \(L\)-series of a modular form of weight 2 at \(s=2\). Applications of the formula to computing Mahler measures are discussed.


11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11F11 Holomorphic modular forms of integral weight
11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
11R27 Units and factorization


PARI/GP; SageMath
Full Text: DOI arXiv


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