On the zeros of Eisenstein series for ${\Gamma }_0^{\ast }(5)$ and ${\Gamma }_0^{\ast }(7)$

Abstract

We locate almost all the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.

15 pages. http://researchmap.jp/j_shigezumi/. arXiv admin note: substantial text overlap with arXiv:math/0607247

References in corpus (1)

• On the zeros of Eisenstein series for ${\Gamma }_0^{\ast }(2)$ and ${\Gamma }_0^{\ast }(3)$

Cited by in corpus (5)

• Zeros of certain combinations of Eisenstein series of weight 2k, 3k, and k + l
• On the zeros of weakly holomorphic modular forms
• Zeros of some level 2 Eisenstein series
• On generalized modular forms supported on cuspidal and elliptic points
• Weakly holomorphic modular forms for some moonshine groups