Hi, 


Could anyone explain to me how A and B are the same/different/equivalent?


A = The Siegel-Walfisz Theorem as stated in Wikipedia (this is the statement in Davenport)


<http://en.wikipedia.org/wiki/Siegel%E2%80%93Walfisz_theorem>


B = The Siegel-Walfisz Theorem with the error term replaced by $x/(\log x)^A$ (see, for example, Iwaniec/Kowalski page 124/419)


Thanks very much.



Siegel-Walfisz Theorem
Version A is stronger, while Version B is easier to state as it has no condition on $q$.


Version A is usually derived from a result of Page which gives even more information (in terms of possible Siegel zeros). See Corollary 11.17 in Montgomery-Vaughan: Multiplicative number theory I.


