Distinguishing Hecke eigenforms

Murty, M.; Pujahari, Sudhir

doi:10.1090/proc/13446

Distinguishing Hecke eigenforms
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by M. Ram Murty and Sudhir Pujahari PDF

Proc. Amer. Math. Soc. 145 (2017), 1899-1904 Request permission

Abstract:

Let $f_1, f_2$ be two distinct normalized Hecke eigenforms of weights $k_1$ and $k_2$ with at least one of them not of CM type and with $p$-th Hecke eigenvalues given by $a_p(f_1)p^{(k_1-1)/2}$ and $a_p(f_2) p^{(k_2-1)/2}$ respectively and $p$ being prime. If $a_p(f_1) = a_p(f_2)$ for a set of primes with positive upper density, then we show that $f_1 = f_2 \otimes \chi$ for some Dirichlet character $\chi$.

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