Let $\chi_{2,q}$ be the real Dirichlet character modulo a prime $q>2$, which is not the principal one (the so-called Legendre symbol). Is it true that $$ \sum_{n=0}^{+\infty} \frac{\chi_{2,q}(n)}{n} > 0 $$ ? How can I prove it?
2026-03-25 19:03:24.1774465404
Summation of Legendre symbol
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