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Subhajit Jana
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If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{x\le p\le 2x}|\lambda_f(p)|^2?$$

To avoid Confusion $$(T_pf)(z)=\frac{1}{\sqrt{p}}\left[\sum_{b=0}^{p-1}f\left(\frac{z+b}{p}\right)+f(pz)\right]$$ Any referecne would be highly helpful.

If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{x\le p\le 2x}|\lambda_f(p)|^2?$$ Any referecne would be highly helpful.

If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{x\le p\le 2x}|\lambda_f(p)|^2?$$

To avoid Confusion $$(T_pf)(z)=\frac{1}{\sqrt{p}}\left[\sum_{b=0}^{p-1}f\left(\frac{z+b}{p}\right)+f(pz)\right]$$ Any referecne would be highly helpful.

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Subhajit Jana
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If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{p\le x}|\lambda_f(p)|^2?$$$$S(x) = \sum_{x\le p\le 2x}|\lambda_f(p)|^2?$$ Any referecne would be highly helpful.

If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{p\le x}|\lambda_f(p)|^2?$$ Any referecne would be highly helpful.

If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{x\le p\le 2x}|\lambda_f(p)|^2?$$ Any referecne would be highly helpful.

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Subhajit Jana
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Lower bound of Hecke eigenvalues of Maass form

If $f$ is a Maass form and $p$-Hecke eigenvalue (i.e. Hecke eigenvalue of usual Hecke operator $T_p$) of $f$ is $\lambda_f(p)$, do we know anything about lower bound of the sum$$S(x) = \sum_{p\le x}|\lambda_f(p)|^2?$$ Any referecne would be highly helpful.