Distinguishing Hecke eigenforms

2010/04/27 by Ghitza, Alexandru · 3 citations
#11-04 (Secondary) #11F11 (Primary) 11F25 #11F30 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1004.4705

Abstract

We revisit a theorem of Ram Murty about the number of initial Fourier coefficients that two cuspidal eigenforms of different weights can have in common. We prove an explicit upper bound on this number, and give better conditional and unconditional asymptotic upper bounds. Finally, we describe a numerical experiment testing the sharpness of the upper bound in the case of forms of level one.

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• Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients
• Determining newforms via arithmetic relations among Fourier coefficients
• Distinguishing Siegel modular forms

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