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A sum related to the first moment of quadratic $L$-functions at $s=1$
Let $(\frac{m}{n})$ be the Jacobi quadratic symbol defined for positive squarefree odd integers $n,m$. Does the following sum go to infinity?
$$
\sum_{1\leq n \leq (\log x)^{100} } \mu^2(2n) \sum_{(\l …