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Zudilin, Wadim

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

Math. Proc. Camb. Philos. Soc. 156, No. 2, 313-326 (2014).
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.

Cited in 2 Reviews
Cited in 15 Documents

MSC:

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

Keywords:

Mahler measure; modular unit; \(L\)-series; modular form

Software:

SageMath; PARI/GP
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\textit{W. Zudilin}, Math. Proc. Camb. Philos. Soc. 156, No. 2, 313--326 (2014; Zbl 1386.11129)
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References:

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