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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 2024 MCQ for Mathematics of Computation is 1.78.

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On Wendt’s determinant
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by Charles Helou PDF
Math. Comp. 66 (1997), 1341-1346 Request permission

Abstract:

Wendt’s determinant of order $m$ is the circulant determinant $W_{m}$ whose $(i,j)$-th entry is the binomial coefficient $\binom m{|i-j|}$, for $1\leq i,j\leq m$. We give a formula for $W_{m}$, when $m$ is even not divisible by 6, in terms of the discriminant of a polynomial $T_{m+1}$, with rational coefficients, associated to $(X+1)^{m+1}-X^{m+1}-1$. In particular, when $m=p-1$ where $p$ is a prime $\equiv -1 (mod 6)$, this yields a factorization of $W_{p-1}$ involving a Fermat quotient, a power of $p$ and the 6-th power of an integer.
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Additional Information
  • Charles Helou
  • Affiliation: Penn State University, Delaware County, 25 Yearsley Mill Road, Media, Pennsylvania 19063
  • Email: cxh22@psu.edu
  • Received by editor(s): May 6, 1996
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 1341-1346
  • MSC (1991): Primary {11C20; Secondary 11Y40, 11D41, 12E10}
  • DOI: https://doi.org/10.1090/S0025-5718-97-00870-3
  • MathSciNet review: 1423075