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The Prime Number Theorem is a theorem that describes the distribution of the primes. It says that the number of primes less than or equal to a real number $x$ is asymptotic to $\frac{x}{\ln x}$.

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A lower-bound for the square-mean of Fourier coefficients of cusp forms at primes argument

There is a basis question which puzzles me for a while. The question is the following: Let $X\ge 2,$ and $\lambda(n)$ be the $n$-th Fourier coefficient of a $GL(2)$ newform of prime level $N>1$, with …
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