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Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero, David Joshua Thornton

Theses and Dissertations

Let N ∈ {8,9,16,25} and let M^#₀(N) be the space of level N weakly holomorphic modular functions with poles only at the cusp at infinity. We explicitly construct a canonical basis for M^#₀(N) indexed by the order of the pole at infinity and show that many of the coefficients of the elements of these bases are divisible by high powers of the prime dividing the level N. Additionally, we show that these basis elements satisfy an interesting duality property. We also give an argument that extends level 1 results …