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Results tagged with cv.complex-variables
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user 9232
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
1
vote
2
answers
129
views
Bounds of zeta function near $\Re(s)=1$
Richert proved in
https://link.springer.com/article/10.1007/BF01399533
that $$ \zeta(s) =O\left( |\Im(s)|^{100(1-\Re(s))^{3/2}} (\log |\Im(s)|)^{2/3}\right)$$ uniformly in the region $\Re(s)\in [1/2,1 …
- 3,062
3
votes
0
answers
187
views
Riemann's explicit formula for square-free numbers
We know that for $x$ being a half-integer $$\sum_{n\leq x}\Lambda(n)=x-\sum_{\rho}\frac{x^\rho}{\rho}+O(1).$$
Is there a similar formula for $\sum_{n\leq x}\mu(n)^2$ in the literature? The underlying …
- 3,062