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On the Zeros of the Miller Basis of Cusp Forms.

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Bibliographic Details
Title: On the Zeros of the Miller Basis of Cusp Forms.
Authors: Raveh, Roei1 (AUTHOR) roeiraveh@mail.tau.ac.il
Source: Research in Number Theory. 10/28/2025, Vol. 11 Issue 4, p1-32. 32p.
Subject Terms: *MODULAR forms, *MATHEMATICAL bounds, *PARAMETERIZATION, *ZERO (The number), *INFINITY (Mathematics), *MATHEMATICS
Abstract: We study the zeros of cusp forms in the Miller basis whose vanishing order at infinity is a fixed number m. We show that for sufficiently large weights, the finite zeros of such forms in the fundamental domain, all lie on the circular part of the boundary of the fundamental domain. We further show and quantify an effective bound for the weight, which is linear in terms of m. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:We study the zeros of cusp forms in the Miller basis whose vanishing order at infinity is a fixed number m. We show that for sufficiently large weights, the finite zeros of such forms in the fundamental domain, all lie on the circular part of the boundary of the fundamental domain. We further show and quantify an effective bound for the weight, which is linear in terms of m. [ABSTRACT FROM AUTHOR]
ISSN:25220160
DOI:10.1007/s40993-025-00679-x