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Results tagged with lower-bounds
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user 38624
2
votes
Accepted
A lower bound on the $L^2$ norm of a Dirichlet polynomial
There may be no such bound if $\alpha$ and $\beta$ are suitably large. For example, using the first derivative test (see e.g. Titchmarsh Chapter 4)
one can see that if $T\le t\le 2T$ then
$$
\sum_{ …
- 43.7k
16
votes
Accepted
Lower bounds on the error term of the prime number theorem
Littlewood proved that
$$
\psi(x)-x = \Omega_{\pm}(x^{\frac 12} \log \log \log x);
$$
here $\Omega_{\pm}$ means that the LHS infinitely often gets as large as a positive constant times the RHS, a …
- 43.7k