A Note on the Transcendence of Zeros of a Certain Family of Weakly Holomorphic Forms Public Deposited

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  • Abstract. Recently, Duke and Jenkins have studied a certain family of modular forms fk,m, that form a natural basis of the space of weakly holomorphic modular forms of weight k on SL2(Z). In particular, they prove that for all but at most [k/12] + 1 values of m, the zeros of these functions all lie on the unit circle. Using a method of Kohnen, we observe that other than i, ρ, these zeros are transcendental. In addition we observe that in the remaining cases there are at most finitely many algebraic zeros and examine the values algebraic zeros in a special case.
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  • Jennings-Shaffer, C., & Swisher, H. (2014). A Note on the Transcendence of Zeros of a Certain Family of Weakly Holomorphic Forms. International Journal of Number Theory, 10(2), 309. doi:10.1142/S1793042113500942
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  • This is an author's peer-reviewed final manuscript, as accepted by the publisher.

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