Deligne's conjecture and mirror symmetry
The author studies the connections between the mirror symmetry of Calabi-Yau threefolds and Deligne's conjecture on the special values of the \(L\)-functions of critical motives. He develops a method to compute Deligne's periods of Calabi-Yau threefolds in a one parameter mirror family. Using this method, the author computes Deligne's period for two crucial examples. Finally, some open problems are discussed in this paper.
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