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On certain unbounded multiplicative functions in short intervals.

Authors :
Zhou, Y.
Source :
Acta Mathematica Hungarica. Aug2024, Vol. 173 Issue 2, p317-339. 23p.
Publication Year :
2024

Abstract

Recently, Mangerel extended the Matomäki–Radziwiłł theorem to a large collection of unbounded multiplicative functions in typical short intervals. In this paper, we combine Mangerel's result with Halász-type result recently established by Granville, Harper and Soundararajan to consider the distribution of a class of multiplicative functions in short intervals. First, we prove cancellation in the sum of the coefficients of the standard L-function of an automorphic irreducible cuspidal representation of GL m over Q with unitary central character in typical intervals of length h (log X) c with h = h (X) → ∞ and some constant c > 0 (under Vinogradov–Korobov zero-free region and GRC). Then we also establish a non-trivial bound for the product of divisor-bounded multiplicative functions with the Liouville function in arithmetic progressions over typical short intervals. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02365294
Volume :
173
Issue :
2
Database :
Academic Search Index
Journal :
Acta Mathematica Hungarica
Publication Type :
Academic Journal
Accession number :
179460624
Full Text :
https://doi.org/10.1007/s10474-024-01457-4