Evaluating prime power Gauss and Jacobi sums
2017 ◽
Vol 48
(3)
◽
pp. 227-240
◽
Keyword(s):
We show that for any mod $p^m$ characters, $\chi_1, \dots, \chi_k,$ with at least one $\chi_i$ primitive mod $p^m$, the Jacobi sum, $$ \mathop{\sum_{x_1=1}^{p^m}\dots \sum_{x_k=1}^{p^m}}_{x_1+\dots+x_k\equiv B \text{ mod } p^m}\chi_1(x_1)\cdots \chi_k(x_k), $$ has a simple evaluation when $m$ is sufficiently large (for $m\geq 2$ if $p\nmid B$). As part of the proof we give a simple evaluation of the mod $p^m$ Gauss sums when $m\geq 2$ that differs slightly from existing evaluations when $p=2$.
1999 ◽
Vol 87
(1)
◽
pp. 74-119
◽
2014 ◽
Vol 10
(08)
◽
pp. 2097-2114
◽
Keyword(s):
2010 ◽
Vol 06
(06)
◽
pp. 1329-1347
◽
2018 ◽
Vol 2018
(741)
◽
pp. 67-86
Keyword(s):
1989 ◽
Vol 46
(3)
◽
pp. 371-383
◽
Keyword(s):