Geodesic
On R. Chapman's “evil determinant”: case $p\equiv 1\pmod4$
Maxim Vsemirnov1
1 St. 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
Acta Arithmetica, Tome 159 (2013) no. 4, pp. 331-344.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $C_{ij}=\genfrac {(}{)}{}{1}{j-i}{p}$.
DOI : 10.4064/aa159-4-3
Keywords: equiv mod prove formula conjectured chapman determinant frac times frac matrix genfrac j i

Maxim Vsemirnov 1

1 St. 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 
@article{10_4064_aa159_4_3,
     author = {Maxim Vsemirnov},
     title = {On {R.} {Chapman's} {\textquotedblleft}evil determinant{\textquotedblright}: case $p\equiv 1\pmod4$},
     journal = {Acta Arithmetica},
     pages = {331--344},
     publisher = {mathdoc},
     volume = {159},
     number = {4},
     year = {2013},
     doi = {10.4064/aa159-4-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa159-4-3/}
}
TY  - JOUR
AU  - Maxim Vsemirnov
TI  - On R. Chapman's “evil determinant”: case $p\equiv 1\pmod4$
JO  - Acta Arithmetica
PY  - 2013
SP  - 331
EP  - 344
VL  - 159
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa159-4-3/
DO  - 10.4064/aa159-4-3
LA  - en
ID  - 10_4064_aa159_4_3
ER  - 
%0 Journal Article
%A Maxim Vsemirnov
%T On R. Chapman's “evil determinant”: case $p\equiv 1\pmod4$
%J Acta Arithmetica
%D 2013
%P 331-344
%V 159
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa159-4-3/
%R 10.4064/aa159-4-3
%G en
%F 10_4064_aa159_4_3
Maxim Vsemirnov. On R. Chapman's “evil determinant”: case $p\equiv 1\pmod4$. Acta Arithmetica, Tome 159 (2013) no. 4, pp. 331-344. doi : 10.4064/aa159-4-3. http://geodesic.mathdoc.fr/articles/10.4064/aa159-4-3/

Cité par Sources :