ON THE ASYMPTOTIC DISTRIBUTION OF ZEROS OF MODULAR FORMS
By Z. Rudnick. 2005
91 citations recorded by the source corpus.
We study the distribution of zeros of holomorphic modular forms. Assuming the Generalized Riemann Hypothesis we show that the zeros of Hecke eigenforms for the modular group become equidistributed with respect to the hyperbolic measure on the modular domain as the weight grows.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/96a3a9325461afb0714906f886ced38d222151f4
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Equidistribution Of Cusp Forms In The Level Aspect (2010, background): “emark 1.5. One cannot relax entirely the restriction of Theorem 1.3 to newforms, since for instance a cusp form of level 1 may be regarded as an oldform of arbitrary level q>1. Remark 1.6. Rudnick [29] showed that Theorem 1.1 implies that the zeros of newforms of level 1 and weight k→∞equidistrib”
- Transcendental values of certain Eichler integrals (2011, methodology): “In this context, we refer to the papers [2, 11, 18, 22, 29–31, 33], where zeros of modular forms have been studied.”
- Mass equidistribution for Hecke eigenforms (2008, unknown): “The Rudnick-Sarnak conjecture in this context states that as k → ∞, for every Hecke eigencuspform f the measure µf tends to the uniform distribution measure.”
- Real zeros of holomorphic Hecke cusp forms (2011, background): “Ghosh and Peter Sarnak One of the striking consequences of the recent proof of the holomorphic QUE conjecture by Holowinsky and Soundararajan [HS] is that Z(f) is equidistributed in X as k!1(see also [Ru] and the report [Sa-2] for a discussion). That is for any nice set ˆX jZ(f) \ j jZ(f)j ! Area( )”