Beyond the Erdős discrepancy problem in function fields
Beyond the Erdős discrepancy problem in function fields
Abstract We characterize the limiting behavior of partial sums of multiplicative functions $$f:\mathbb {F}_q[t]\rightarrow S^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>t</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:math> . In contrast to the number field setting, the characterization depends crucially on whether …