The effective Chebotarev density theorem and modular forms modulo 𝔪

Lichtenstein, Sam

doi:10.1090/S0002-9939-08-09333-7

The effective Chebotarev density theorem and modular forms modulo $\mathfrak m$
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Proc. Amer. Math. Soc. 136 (2008), 3419-3428 Request permission

Abstract:

Suppose that $f$ (resp. $g$) is a modular form of integral (resp. half-integral) weight with coefficients in the ring of integers $\mathcal {O}_K$ of a number field $K$. For any ideal $\mathfrak {m}\subset \mathcal {O}_K$, we bound the first prime $p$ for which $f\mid T_p$ (resp. $g\mid T_{p^2}$) is zero ($\mod \mathfrak {m}$). Applications include the solution to a question of Ono (2001) concerning partitions.

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