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https://terrytao.wordpress.com/2014...unction-and-the-functional-equation-optional/

Can someone help me linking Corollary 2 to Theorem 1?

I am just a amateurish layman who tries to piece things together from various sources from the net. So I got confused when I found out that people use two different forms of the functional equation.

Any help, hints or links are very much appreciated!