PreprintarXiv licencearXiv
Upper bounds on the number of images produced by point-mass lenses at different distances
Abstract
If a light source is sequentially lensed by n intervening point-mass lenses at distinct distances, the number of isolated images for a generic source position cannot be greater than 2· 3n−1. If lensing shear is present in each lens plane, the image counts could be as large as 4n, however. For a general multi-plane point-mass lens system, we also devise the recurrence for the BKK bound on the image counts, which is strictly less than Perry's bound due to the resultant degree for n≥ 2. None the less, this bound is still quadratic in the number of lenses on each plane, so is likely to overestimate the true sharp bound, which is expected to grow linearly with the number of lenses.
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BibTeX
@misc{an2026upper,
title = {{Upper bounds on the number of images produced by point-mass lenses at different distances}},
author = {J. An},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25594},
eprint = {2610.25594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25594},
}
RIS
TY - UNPB
TI - Upper bounds on the number of images produced by point-mass lenses at different distances
AU - J. An
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25594
UR - https://arxiv.org/abs/2610.25594
AB - If a light source is sequentially lensed by n intervening point-mass lenses at distinct distances, the number of isolated images for a generic source position cannot be greater than 2· 3^n−1. If lensing shear is present in each lens plane, the image counts could be as large as 4^n, however. For a general multi-plane point-mass lens system, we also devise the recurrence for the BKK bound on the image counts, which is strictly less than Perry's bound due to the resultant degree for n≥ 2. None the less, this bound is still quadratic in the number of lenses on each plane, so is likely to overestimate the true sharp bound, which is expected to grow linearly with the number of lenses.
ER -