On the interlacing of the zeros of certain Poincaré cusp forms

Dhillon, Sonika; kala, D.Sasi; Saha, Ekata

doi:10.1016/j.jmaa.2023.127540

Journal of Mathematical Analysis and Applications

2023

DOI: 10.1016/j.jmaa.2023.127540

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On the interlacing of the zeros of certain Poincaré cusp forms

Sonika Dhillon

D.Sasi kala

Ekata Saha

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2024

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Asymptotic Zeros of Poincaré Series

Kimmel

2024

International Mathematics Research Notices

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We study the zeros of Poincaré series $P_{k,m}$ for the full modular group. We consider the case where $m \sim \alpha k$ for some constant $\alpha> 0$. We show that in this case a positive proportion of the zeros lie on the line $\frac{1}{2} + it$. We further show that if $\alpha> \frac{\log (2)}{2\pi }$ then the imaginary axis also contains a positive proportion of zeros. We also give a description for the location of the non-real zeros when $\alpha $ is small.

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Asymptotic Zeros of Poincaré Series

Kimmel

2024

International Mathematics Research Notices

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On the interlacing of the zeros of certain Poincaré cusp forms

Cited by 1 publication

References 8 publications

Asymptotic Zeros of Poincaré Series

Asymptotic Zeros of Poincaré Series

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