Jacobsthal identity for Q(√ - 2)

Ki Ichiro Hashimoto; Ling Long; Yifan Yang

doi:10.1515/FORM.2011.102

Jacobsthal identity for Q(√ - 2)

Ki Ichiro Hashimoto^*, Ling Long, Yifan Yang

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let p be a prime congruent to 1 or 3 modulo 8 so that the equation p = a ² C 2b ² is solvable in integers. In this paper, we obtain closed-form expressions for a and b in terms of Jacobsthal sums. This is analogous to a classical identity of Jacobsthal.

Original language	English
Pages (from-to)	1225-1238
Number of pages	14
Journal	Forum Mathematicum
Volume	24
Issue number	6
DOIs	https://doi.org/10.1515/FORM.2011.102
Publication status	Published - 2012 Nov 1

Keywords

Hyperelliptic curve
Jacobsthal sum
L-function

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1515/FORM.2011.102

Cite this

@article{a6e89a4dd90c487a94e926503c740aa6,

title = "Jacobsthal identity for Q(√ - 2)",

abstract = "Let p be a prime congruent to 1 or 3 modulo 8 so that the equation p = a 2 C 2b 2 is solvable in integers. In this paper, we obtain closed-form expressions for a and b in terms of Jacobsthal sums. This is analogous to a classical identity of Jacobsthal.",

keywords = "Hyperelliptic curve, Jacobsthal sum, L-function",

author = "Hashimoto, {Ki Ichiro} and Ling Long and Yifan Yang",

year = "2012",

month = nov,

day = "1",

doi = "10.1515/FORM.2011.102",

language = "English",

volume = "24",

pages = "1225--1238",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH & Co. KG",

number = "6",

}

TY - JOUR

T1 - Jacobsthal identity for Q(√ - 2)

AU - Hashimoto, Ki Ichiro

AU - Long, Ling

AU - Yang, Yifan

PY - 2012/11/1

Y1 - 2012/11/1

N2 - Let p be a prime congruent to 1 or 3 modulo 8 so that the equation p = a 2 C 2b 2 is solvable in integers. In this paper, we obtain closed-form expressions for a and b in terms of Jacobsthal sums. This is analogous to a classical identity of Jacobsthal.

AB - Let p be a prime congruent to 1 or 3 modulo 8 so that the equation p = a 2 C 2b 2 is solvable in integers. In this paper, we obtain closed-form expressions for a and b in terms of Jacobsthal sums. This is analogous to a classical identity of Jacobsthal.

KW - Hyperelliptic curve

KW - Jacobsthal sum

KW - L-function

UR - http://www.scopus.com/inward/record.url?scp=84870182669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870182669&partnerID=8YFLogxK

U2 - 10.1515/FORM.2011.102

DO - 10.1515/FORM.2011.102

M3 - Article

AN - SCOPUS:84870182669

SN - 0933-7741

VL - 24

SP - 1225

EP - 1238

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 6

ER -

Jacobsthal identity for Q(√ - 2)

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this