We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8277-11-2015, author = {Deniz A. Kaptan}, title = {A note on small gaps between primes in arithmetic progressions}, journal = {Acta Arithmetica}, volume = {172}, year = {2016}, pages = {351-375}, zbl = {1337.11061}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8277-11-2015} }
Deniz A. Kaptan. A note on small gaps between primes in arithmetic progressions. Acta Arithmetica, Tome 172 (2016) pp. 351-375. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8277-11-2015/