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

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/v692tb83f

Descriptions

Attribute Name	Values
Creator	Jennings-Shaffer, Chris Swisher, Holly
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.
Resource Type	Article
DOI	https://doi.org/10.1142/S1793042113500942
Date Available	2014-09-23T08:00:10+00:00
Date Issued	2014-03
Citation	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
Journal Title	International Journal of Number Theory
Journal Volume	10
Journal Issue/Number	2
Dichiarazione dei diritti	Copyright Not Evaluated
Related Items	The published article can be found at the International Journal of Number Theory.
Publisher	World Scientific Publishing Co.
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/51982
Additional Information	This is an author's peer-reviewed final manuscript, as accepted by the publisher.