Interlacing property of the zeros of $j_n(\tau )$
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- by Jonas Jermann PDF
- Proc. Amer. Math. Soc. 140 (2012), 3385-3396 Request permission
Abstract:
We improve an estimate for $j_n(\tau )$ on the unit circle and use it to prove an interlacing property of the zeros of $j_n(\tau )$.References
- Tetsuya Asai, Masanobu Kaneko, and Hirohito Ninomiya, Zeros of certain modular functions and an application, Comment. Math. Univ. St. Paul. 46 (1997), no. 1, 93–101. MR 1448475
- W. Duke and Paul Jenkins, On the zeros and coefficients of certain weakly holomorphic modular forms, Pure Appl. Math. Q. 4 (2008), no. 4, Special Issue: In honor of Jean-Pierre Serre., 1327–1340. MR 2441704, DOI 10.4310/PAMQ.2008.v4.n4.a15
- M. Kaneko and D. Zagier, Supersingular $j$-invariants, hypergeometric series, and Atkin’s orthogonal polynomials, Computational perspectives on number theory (Chicago, IL, 1995) AMS/IP Stud. Adv. Math., vol. 7, Amer. Math. Soc., Providence, RI, 1998, pp. 97–126. MR 1486833, DOI 10.1090/amsip/007/05
- Hiroshi Nozaki, A separation property of the zeros of Eisenstein series for $\textrm {SL}(2,\Bbb Z)$, Bull. Lond. Math. Soc. 40 (2008), no. 1, 26–36. MR 2409175, DOI 10.1112/blms/bdm117
- R. A. Rankin, The zeros of certain Poincaré series, Compositio Math. 46 (1982), no. 3, 255–272. MR 664646
- F. K. C. Rankin and H. P. F. Swinnerton-Dyer, On the zeros of Eisenstein series, Bull. London Math. Soc. 2 (1970), 169–170. MR 260674, DOI 10.1112/blms/2.2.169
Additional Information
- Jonas Jermann
- Affiliation: Department of Mathematics, ETH Zurich, Ramistrasse 101, 8092 Zurich, Switzerland
- Email: jjermann@math.ethz.ch
- Received by editor(s): August 9, 2010
- Received by editor(s) in revised form: April 12, 2011
- Published electronically: February 22, 2012
- Communicated by: Kathrin Bringmann
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3385-3396
- MSC (2010): Primary 11F11; Secondary 11F03
- DOI: https://doi.org/10.1090/S0002-9939-2012-11212-2
- MathSciNet review: 2929008