39116
It improves Dirichlet 's theorem on prime numbers in arithmetic progressions , by showing that by averaging over the modulus over a range , the mean error is much less than can be proved in a given case .
 person: Dirichlet
Given options, please tell me the categories of all the listed entity words.Output format is "type1: word1; type2: word2". 
Option: location, person, organization 
Text: {0} 
 Entities: Dirichlet 
Answer:
 person: Dirichlet