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On R. Chapman's “evil determinant”: case $p\equiv 1\pmod4$

Volume 159 / 2013

Maxim Vsemirnov Acta Arithmetica 159 (2013), 331-344 MSC: Primary 11C20; Secondary 11R29, 15A15, 15B05. DOI: 10.4064/aa159-4-3

Abstract

For $p\equiv 1\ ({\rm mod}\,4)$, we prove the formula (conjectured by R. Chapman) for the determinant of the $\frac {p+1}{2}\times \frac {p+1}{2}$ matrix $C=(C_{ij})$ with $C_{ij}=\genfrac {(}{)}{}{1}{j-i}{p}$.

Authors

  • Maxim VsemirnovSt. Petersburg Department of
    V. A. Steklov Institute of Mathematics
    27 Fontanka
    St. Petersburg, 191023, Russia
    and
    Department of Mathematics and Mechanics
    St. Petersburg State University
    28 University prospekt
    St. Petersburg, 198504, Russia
    e-mail

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