RELATION BETWEEN A MOCK MODULAR FORM AND ITS SHADOW THROUGH LIMIT VALUES

초록

. In his last letter to Hardy, Ramanujan defined 17 mock theta functions, and Zwegers discovered that they are holomorphic parts of harmonic weak Maass forms of weight 21. Zagier defined a mock modular form as the holomorphic part of a harmonic weak Maass form F. The nonholomorphic part of F can be obtained by the nonholomorphic Eichler integral of a cusp form, which is called the shadow. In this paper, we study the relation between a mock modular form and its shadow through limit values of a mock modular form when a mock modular form has weight k is an element of 21Z such that k <= -2.

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