Gauss and Jacobi Sums

1982 ◽  
pp. 88-107 ◽  
Author(s):  
Kenneth Ireland ◽  
Michael Rosen
Keyword(s):  
Jacobi Sums ◽  
Gauss And Jacobi Sums

scholarly journals Evaluating prime power Gauss and Jacobi sums

2017 ◽  
Vol 48 (3) ◽  
pp. 227-240 ◽  
Author(s):  
Misty Ostergaard ◽  
Vincent Pigno ◽  
Christopher Pinner
Keyword(s):  
Prime Power ◽  
Gauss Sums ◽  
Jacobi Sums ◽  
Jacobi Sum ◽  
Simple Evaluation ◽  
Gauss And Jacobi Sums ◽  
Mod P

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 $p=2$.

Gauss and Jacobi Sums

1999 ◽  
Vol 83 (497) ◽  
pp. 349
Author(s):  
Peter Cass ◽  
Bruce C. Berndt ◽  
Ronald J. Evans ◽  
Kenneth S. Williams
Keyword(s):  
Jacobi Sums ◽  
Gauss And Jacobi Sums

scholarly journals Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999 ◽  
Vol 87 (1) ◽  
pp. 74-119 ◽  
Author(s):  
Ronald Evans ◽  
Henk D.L. Hollmann ◽  
Christian Krattenthaler ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Gauss Sums ◽  
Cyclic Difference Sets ◽  
Jacobi Sums

scholarly journals Perfect difference systems of sets and Jacobi sums

2009 ◽  
Vol 309 (12) ◽  
pp. 3954-3961 ◽  
Author(s):  
Ryoh Fuji-Hara ◽  
Koji Momihara ◽  
Mieko Yamada
Keyword(s):  
Jacobi Sums ◽  
Difference Systems ◽  
Difference Systems Of Sets

scholarly journals On mean convergence of Fourier-Jacobi series

2021 ◽  
Vol 15 ◽  
pp. 70
Author(s):  
S.V. Goncharov ◽  
V.P. Motornyi
Keyword(s):  
Lebesgue Constants ◽  
Order Of Growth ◽  
Jacobi Series ◽  
Jacobi Sums ◽  
Mean Convergence

We establish the order of growth of modified Lebesgue constants of Fourier-Jacobi sums in $L_{p,w}$ spaces.

scholarly journals Reciprocity and Jacobi sums

1967 ◽  
Vol 20 (2) ◽  
pp. 275-280
Author(s):  
Joseph Muskat
Keyword(s):  
Jacobi Sums

Homology of the Fermat Tower and Universal Measures for Jacobi Sums

2016 ◽  
Vol 59 (3) ◽  
pp. 624-640
Author(s):  
Noriyuki Otsubo
Keyword(s):  
Power Series ◽  
Group Ring ◽  
Simple Proof ◽  
Homology Group ◽  
Interpolation Property ◽  
Cyclic Module ◽  
Precise Description ◽  
Fermat Curve ◽  
Jacobi Sums ◽  
Definition Of

AbstractWe give a precise description of the homology group of the Fermat curve as a cyclic module over a group ring. As an application, we prove the freeness of the profinite homology of the Fermat tower. This allows us to define measures, an equivalent of Anderson’s adelic beta functions, in a manner similar to Ihara’s definition of ℓ-adic universal power series for Jacobi sums. We give a simple proof of the interpolation property using a motivic decomposition of the Fermat curve.

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