Exercising in complex Mahler measures: diamonds are not forever

Autor:	Ringeling, Berend, Zudilin, Wadim
Rok vydání:	2021
Předmět:	Mathematics - Number Theory Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables Mathematics - K-Theory and Homology Primary 11R06 Secondary 11G05 33C75 33E05
Druh dokumentu:	Working Paper
Popis:	Recently, Hang Liu and Hourong Qin came up with a numerical observation about the relation between the Mahler measures of one hyperelliptic and two elliptic families. The discoverers foresee a proof of the identities "by extending ideas in" two papers of Matilde Lal\'{\i}n and Gang Wu, the ideas based on a theorem of Spencer Bloch and explicit diamond-operation calculations on the underlying curves. We prove the relation using the already available diamond-free methodology. While finding such relations for the Mahler measures remains an art, proving them afterwards is mere complex (analysis) exercising. Comment: 5 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.14380 Zobrazit plný text záznamu View this record from Arxiv