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math.NT2021
Quadrics in arithmetic statistics
Levent Alpöge
We (re)introduce the circle method into arithmetic statistics. More specifically, we combine the circle method with Bhargava's counting technique in order to give a general method…
math.NT2021
Note on a theorem of Professor X
Levent Alpöge
Between his arrival in Frankfurt in and and his proof of his famous finiteness theorem for integral points in , Siegel had no publications. He did, however, write a le…
math.NT2021
Modularity and effective Mordell I
Levent Alpöge
We give an effective proof of Faltings' theorem for curves mapping to Hilbert modular stacks over odd-degree totally real fields. We do this by giving an effective proof of the Sha…