Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The sum of reciprocal of zeroes of riemann zeta function converges conditionally that if they are paired as $\rho $ and $1-\rho$ My question is if the sum still converges if they are paired as $\rho$ and $\rho$ conjugate .

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Yes. $\textbf{}$ $\textbf{}$ $\textbf{}$

share|improve this answer
Both convergence arguments rely on the fact that $\sum_\rho 1/(\Im\rho)^2$ converges, which is a consequence of the upper bound $cT\log T$ for the number of zeros with imaginary part bounded in absolute value by $T$. Then, note $1/\rho+1/\bar\rho = 2\Re\rho/((\Re\rho)^2+(\Im\rho)^2) \le 2/(\Im\rho)^2$. –  Greg Martin Nov 28 '13 at 7:28
I fixed the awkward spacing before the period. I hope you don't mind. –  Potato Nov 28 '13 at 7:29
Not at all. The awkwardness should all come from the content! –  Greg Martin Nov 28 '13 at 7:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.