  It is well known, General Riemann Hypothesis have many equivalent
propositions. In this paper, we will prove an equivalent proposition that is
related to the prime theorem for arithmetic series. However, the prime theorem
for arithmetic series can be represented as the sieve functions. In order to
improve the sieve method, we introduced the transformation of sieve function.
For this, we obtain some useful lemmas. The difference of similar sieve
functions will be determined within a certain range. Furthermore, we proved the
equivalent proposition of General Riemann Hypothesis. So we proved General
Riemann Hypothesis and Riemann Hypothesis to be true.
