On Viazovska’s modular form inequalities

Viazovska proved that the [Formula: see text] lattice sphere packing is the densest sphere packing in [Formula: see text] dimensions. Her proof relies on two inequalities between functions defined in terms of modular and quasimodular forms. We give a direct proof of these inequalities that does not...

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Detalles Bibliográficos
Autor principal: Romik, Dan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2023
Materias:
Physical Sciences
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10614599/
https://www.ncbi.nlm.nih.gov/pubmed/37851677
http://dx.doi.org/10.1073/pnas.2304891120
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author Romik, Dan
author_facet Romik, Dan
author_sort Romik, Dan
collection PubMed
description Viazovska proved that the [Formula: see text] lattice sphere packing is the densest sphere packing in [Formula: see text] dimensions. Her proof relies on two inequalities between functions defined in terms of modular and quasimodular forms. We give a direct proof of these inequalities that does not rely on computer calculations.
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spelling pubmed-106145992023-10-31 On Viazovska’s modular form inequalities Romik, Dan Proc Natl Acad Sci U S A Physical Sciences Viazovska proved that the [Formula: see text] lattice sphere packing is the densest sphere packing in [Formula: see text] dimensions. Her proof relies on two inequalities between functions defined in terms of modular and quasimodular forms. We give a direct proof of these inequalities that does not rely on computer calculations. National Academy of Sciences 2023-10-18 2023-10-24 /pmc/articles/PMC10614599/ /pubmed/37851677 http://dx.doi.org/10.1073/pnas.2304891120 Text en Copyright © 2023 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Romik, Dan
On Viazovska’s modular form inequalities
title On Viazovska’s modular form inequalities
title_full On Viazovska’s modular form inequalities
title_fullStr On Viazovska’s modular form inequalities
title_full_unstemmed On Viazovska’s modular form inequalities
title_short On Viazovska’s modular form inequalities
title_sort on viazovska’s modular form inequalities
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10614599/
https://www.ncbi.nlm.nih.gov/pubmed/37851677
http://dx.doi.org/10.1073/pnas.2304891120
work_keys_str_mv AT romikdan onviazovskasmodularforminequalities

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