Zeros of modular forms of half integral weight View Full Text


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Article Info

DATE

2016-12

AUTHORS

Amanda Folsom, Paul Jenkins

ABSTRACT

We study canonical bases for spaces of weakly holomorphic modular forms of level 4 and weights in Z+12 and show that almost all modular forms in these bases have the property that many of their zeros in a fundamental domain for Γ0(4) lie on a lower boundary arc of the fundamental domain. Additionally, we show that at many places on this arc, the generating function for Hurwitz class numbers is equal to a particular mock modular Poincaré series, and show that for positive weights, a particular set of Fourier coefficients of cusp forms in this canonical basis cannot simultaneously vanish. More... »

PAGES

23

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40993-016-0054-6

DOI

http://dx.doi.org/10.1007/s40993-016-0054-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1016739529


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