Back to Search
Start Over
On certain unbounded multiplicative functions in short intervals.
- 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]
- Subjects :
- *ARITHMETIC series
*ARITHMETIC functions
*SAWLOGS
*COLLECTIONS
*L-functions
Subjects
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