Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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
HTML articles powered by AMS MathViewer

by Henry Cohn and Nicholas Triantafillou HTML | PDF
Math. Comp. 91 (2022), 491-508 Request permission


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.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2020): 52C17, 11H31, 11F11
  • Retrieve articles in all journals with MSC (2020): 52C17, 11H31, 11F11
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:
  • 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:
  • 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:
  • MathSciNet review: 4350546