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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Dual linear programming bounds for sphere packing via modular forms
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by Henry Cohn and Nicholas Triantafillou HTML | PDF
Math. Comp. 91 (2022), 491-508 Request permission

Abstract:

We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions $8$ and $24$, where the linear programming bound is sharp, we show that it comes nowhere near the best packing densities known in dimensions $12$, $16$, $20$, $28$, and $32$. More generally, we provide a systematic technique for proving separations of this sort.
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Additional Information
  • Henry Cohn
  • Affiliation: Microsoft Research New England, One Memorial Drive, Cambridge, Massachusetts 02142
  • MR Author ID: 606578
  • ORCID: 0000-0001-9261-4656
  • Email: cohn@microsoft.com
  • Nicholas Triantafillou
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Address at time of publication: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 978350
  • ORCID: 0000-0003-1464-4619
  • Email: nicholas.triantafillou@gmail.com
  • Received by editor(s): September 23, 2019
  • Received by editor(s) in revised form: April 4, 2021
  • Published electronically: July 30, 2021
  • Additional Notes: The second author was partially supported by an internship at Microsoft Research New England, a National Science Foundation Graduate Research Fellowship under grant #1122374, and Simons Foundation grant #550033.
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 491-508
  • MSC (2020): Primary 52C17; Secondary 11H31, 11F11
  • DOI: https://doi.org/10.1090/mcom/3662
  • MathSciNet review: 4350546