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Abstract We give an improved lower bound for the average of the Erdős–Hooley function , namely for all and any fixed , where is an exponent previously appearing in work of Green and the first two authors. This improves on a previous lower bound of of Hall and Tenenbaum, and can be compared to the recent upper bound of of the second and third authors.
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On the spectral large sieve inequality for symmetric-squares
Abstract We improve on the spectral large sieve inequality for symmetric-squares. We also prove a lower bound showing that the most optimistic upper bound is not true for this family.
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- Award ID(s):
- 2302210
- PAR ID:
- 10563288
- Publisher / Repository:
- De Gruyter
- Date Published:
- Journal Name:
- Forum Mathematicum
- Volume:
- 35
- Issue:
- 5
- ISSN:
- 0933-7741
- Page Range / eLocation ID:
- 1221 to 1236
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1515/forum-2022-0229
