Geodesic
CM Periods, CM Regulators, and Hypergeometric Functions, I
Canadian journal of mathematics, Tome 70 (2018) no. 3, pp. 481-514

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DOI

We prove the Gross–Deligne conjecture on CM periods for motives associated with ${{H}^{2}}$ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the ${{K}_{1}}$ -regulators in terms of hypergeometric functions $_{3}{{F}_{2}}$ , and obtain a new example of non-trivial regulators.
DOI : 10.4153/CJM-2017-008-6
Mots-clés : 14D07, 19F27, 33C20, 11G15, 14K22, period, regulator, complex multiplication, hypergeometric function 
Asakura, Masanori; Otsubo, Noriyuki. CM Periods, CM Regulators, and Hypergeometric Functions, I. Canadian journal of mathematics, Tome 70 (2018) no. 3, pp. 481-514. doi: 10.4153/CJM-2017-008-6
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     author = {Asakura, Masanori and Otsubo, Noriyuki},
     title = {CM {Periods,} {CM} {Regulators,} and {Hypergeometric} {Functions,} {I}},
     journal = {Canadian journal of mathematics},
     pages = {481--514},
     year = {2018},
     volume = {70},
     number = {3},
     doi = {10.4153/CJM-2017-008-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-008-6/}
}
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