Regulator of modular units and Mahler measures
Wadim Zudilin
TL;DR
This paper proves a formula linking the regulator of modular units to the L-series of a weight 2 modular form at s=2, with applications to Mahler measures.
Contribution
It provides a proof of Mellit and Brunault's formula connecting regulators of modular units and L-series, enabling new computations of Mahler measures.
Findings
Validated the formula relating regulators and L-series.
Applied the formula to compute specific Mahler measures.
Enhanced understanding of the connection between modular units and Mahler measures.
Abstract
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 -series of a modular form of weight 2 at . Applications of the formula to computing Mahler measures are discussed.
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