Borcherds Lift on the Paramodular Group of Level 3
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This paper deals with Borcherds products on the paramodular group of level 3. After introducing the notation, we present in a more general setting how to construct Borcherds lifts. The approach used in this paper is based on work of V. Gritsenko and V. Nikulin (compare ). In section 3, we will go into more detail on the paramodular group of level 3. We will determine the characters and divisors on this group. Section 4 deals with weakly Jacobi forms of weight 0 and index 3. These functions are of special interest as they are used as input functions for the Borcherds lift which we want to consider. We will learn that it is possible to construct weakly Jacobi forms. Even more, we can influence properties of the Borcherds lift in the construction of weakly Jacobi forms. In Sect. 5, we will calculate the Borcherds lifts of the functions created in Section 4. Moreover, we will examine those Borcherds products and give statements on divisors and characters.
KeywordsBorcherds Lift Paramodular Group Borcherds Products Jacobi Forms Input Function
We would like to thank the referee for valuable suggestions.
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