Gamma-function and Gaussian-sum-function

Helversen-Pasotto, A.. "Gamma-function and Gaussian-sum-function." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1993. [195]-200. <http://eudml.org/doc/220854>.

@inProceedings{Helversen1993,
abstract = {After some remarks about the analogy between the classical gamma-function and Gaussian sums over finite fields a complete, very short explicit proof is given of an identity expressing a certain sum of products of Gaussian sums as a product of Gaussian sums. This identity is an analogue of the classical Barnes’ first lemma for the gamma-function. Four multiplicative characters of a finite field are concerned; the usually necessary restrictions on the triviality of certain products of these characters are avoided by the use of corrective terms. References are given for other approaches of this identity.In [2] a parallel proof is given for the classical identity and its finite analogue; the status of this reference has meanwhile changed from “preprint” to “published”: Can. Math. Bull. 36, No. 3, 273-282 (1993; Zbl 0803.33001), the status of reference [4] has changed from “to appear” into “published”: Suppl. Rend. Circ. Mat. Palermo, II. Ser. 26, 179-188 !},
author = {Helversen-Pasotto, A.},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Geometry; Srní (Czechoslovakia); Physics},
location = {Palermo},
pages = {[195]-200},
publisher = {Circolo Matematico di Palermo},
title = {Gamma-function and Gaussian-sum-function},
url = {http://eudml.org/doc/220854},
year = {1993},
}

TY - CLSWK
AU - Helversen-Pasotto, A.
TI - Gamma-function and Gaussian-sum-function
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1993
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [195]
EP - 200
AB - After some remarks about the analogy between the classical gamma-function and Gaussian sums over finite fields a complete, very short explicit proof is given of an identity expressing a certain sum of products of Gaussian sums as a product of Gaussian sums. This identity is an analogue of the classical Barnes’ first lemma for the gamma-function. Four multiplicative characters of a finite field are concerned; the usually necessary restrictions on the triviality of certain products of these characters are avoided by the use of corrective terms. References are given for other approaches of this identity.In [2] a parallel proof is given for the classical identity and its finite analogue; the status of this reference has meanwhile changed from “preprint” to “published”: Can. Math. Bull. 36, No. 3, 273-282 (1993; Zbl 0803.33001), the status of reference [4] has changed from “to appear” into “published”: Suppl. Rend. Circ. Mat. Palermo, II. Ser. 26, 179-188 !
KW - Proceedings; Geometry; Srní (Czechoslovakia); Physics
UR - http://eudml.org/doc/220854
ER -