On sign changes for almost prime coefficients of half-integral weight modular forms

2015/04/15 by Srilakshmi Krishnamoorthy, M. Ram Murty, Krishnamoorthy, Srilakshmi +1
Mathematics · #11F11 (Primary) #11F30 (Secondary) #11F37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F30 #msc:11F37

paper · pdf · doi:10.48550/arxiv.1504.03948

To appear in Mathematika

openalex publication_date 2015/04/15 · arxiv created 2016/03/21 · arxiv updated 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a half-integral weight modular form f = ∑_n=1^∞ a_f(n)n^(k-1)/(2) qⁿ of weight k = l +(1)/(2) on Γ₀(4) such that a_f(n) (n ∈ ℕ) are real, we prove for a fixed suitable natural number r that a_f(n) changes sign infinitely often as n varies over numbers having at most r prime factors, assuming the analog of the Ramanujan conjecture for half-integral weight forms.

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