Joseph:
1. Collected Essays I and II by Haym Soloveitchik (English)
2. מנהג אשכנז הקדמון , ישראל תא-שמע
3. Criticism and response Soloveitchik-Brody found in Soloveitchik’s personal site
This is a good start, of course there is more
I will not deal here with amateurs who “claim to know” based on biased half-baked sources from different time periods. Anyone familiar with population migration, the founder effect and other phenomena knows that conclusive evidence, DNA or not, is virtually impossible. Furthermore, quantity is worth much less than quality. Simply being an Ashkenazic Jew does not confer influence on the halachah, culture or customs of the entire group. The existence of one Rabbeinu Gershom was far more influential than a hundred post-churban ashkenazic Jews somewhere in Europe.
There are strong arguments on both sides of this debate. The common denominator is that there is a paucity of reliable information on the history of Ashkenazic Jewry. Just for starters, find some reliable information on Rabbeinu Gershom’s teacher, Rabbi Levontin. Other than his Italian name, we know virtually nothing about him.
Only a reading of the books (they are long) will present a more informative picture. Some of the material is in Hebrew, a necessity here. I am also an amateur and I differ to the scholars. But I read them, and they are all worth reading. No shortcuts. The last word has not been spoken .