TY - JOUR
T1 - Möbius cancellation on polynomial sequences and the quadratic Bateman–Horn conjecture over function fields
AU - Sawin, Will
AU - Shusterman, Mark
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/8
Y1 - 2022/8
N2 - We establish cancellation in short sums of certain special trace functions over Fq[u] below the Pólya–Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the Fq[u] -analog of Chowla’s conjecture on cancellation in Möbius sums over polynomial sequences, and of the Bateman–Horn conjecture in degree 2, for some values of q. A final application is to sums of trace functions over primes in Fq[u].
AB - We establish cancellation in short sums of certain special trace functions over Fq[u] below the Pólya–Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the Fq[u] -analog of Chowla’s conjecture on cancellation in Möbius sums over polynomial sequences, and of the Bateman–Horn conjecture in degree 2, for some values of q. A final application is to sums of trace functions over primes in Fq[u].
UR - http://www.scopus.com/inward/record.url?scp=85129814661&partnerID=8YFLogxK
U2 - 10.1007/s00222-022-01115-y
DO - 10.1007/s00222-022-01115-y
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AN - SCOPUS:85129814661
SN - 0020-9910
VL - 229
SP - 751
EP - 927
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -