On singular moduli for level 2 and 3

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Gross and Zagier proved a formula for the absolute norm N(j(α_1) - j(α_2)) of a difference of singular values of the modular function j. We formulate and prove the analogues of their result for a number of functions of level 2 and 3.
This paper is part of my thesis 'Primitive roots and singular moduli'

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