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The paper is devoted to problems at the intersection of formal group theory,the theory of Hirzebruch genera, and the theory of elliptic functions.  The elliptic function of level N determines the elliptic genus of level N asa Hirzebruch genus. It is known that the elliptic function of level N is aspecialization of the Krichever function that determines the Krichever genus.The Krichever function is the exponential of the universal Buchstaber formalgroup.  In this work we describe the rings of coefficients of specializations ofuniversal Buchstaber formal groups that correspond to the elliptic genus oflevel N for N = 2,3,4,5, and 6.

Rings of Coefficients of Universal Formal Groups for Elliptic Genus of Level N