Small Representations by Indefinite Ternary Quadratic Forms

J. B. Friedlander; H. Iwaniec

doi:10.1007/978-1-4614-6642-0_7

Small Representations by Indefinite Ternary Quadratic Forms

J. B. Friedlander
, H. Iwaniec

School of Arts and Sciences, Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

We study nonhomogeneous Pythagorean triples, that is, solutions of the diophantine equation x² + y² - z² = D where D is fixed and non-zero. We are particularly concerned, for D large and positive, with counting the solutions having x, y, z, all small relative to D.

Original language	English (US)
Title of host publication	Number Theory and Related Fields
Subtitle of host publication	In Memory of Alf van der Poorten
Publisher	Springer New York LLC
Pages	157-164
Number of pages	8
ISBN (Print)	9781461466413
DOIs	https://doi.org/10.1007/978-1-4614-6642-0_7
State	Published - 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	43
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/978-1-4614-6642-0_7

Cite this

@inproceedings{e17014010e6b4d89a6b8578c94f4820c,

title = "Small Representations by Indefinite Ternary Quadratic Forms",

abstract = "We study nonhomogeneous Pythagorean triples, that is, solutions of the diophantine equation x2 + y2 - z2 = D where D is fixed and non-zero. We are particularly concerned, for D large and positive, with counting the solutions having x, y, z, all small relative to D.",

author = "Friedlander, \{J. B.\} and H. Iwaniec",

note = "Funding Information: JF was supported in part by NSERC grant A5123; HI was supported in part by NSF grant DMS-1101574.",

year = "2013",

doi = "10.1007/978-1-4614-6642-0\_7",

language = "English (US)",

isbn = "9781461466413",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "157--164",

booktitle = "Number Theory and Related Fields",

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TY - GEN

T1 - Small Representations by Indefinite Ternary Quadratic Forms

AU - Friedlander, J. B.

AU - Iwaniec, H.

N1 - Funding Information: JF was supported in part by NSERC grant A5123; HI was supported in part by NSF grant DMS-1101574.

PY - 2013

Y1 - 2013

N2 - We study nonhomogeneous Pythagorean triples, that is, solutions of the diophantine equation x2 + y2 - z2 = D where D is fixed and non-zero. We are particularly concerned, for D large and positive, with counting the solutions having x, y, z, all small relative to D.

AB - We study nonhomogeneous Pythagorean triples, that is, solutions of the diophantine equation x2 + y2 - z2 = D where D is fixed and non-zero. We are particularly concerned, for D large and positive, with counting the solutions having x, y, z, all small relative to D.

UR - https://www.scopus.com/pages/publications/84883384826

UR - https://www.scopus.com/pages/publications/84883384826#tab=citedBy

U2 - 10.1007/978-1-4614-6642-0_7

DO - 10.1007/978-1-4614-6642-0_7

M3 - Conference contribution

AN - SCOPUS:84883384826

SN - 9781461466413

T3 - Springer Proceedings in Mathematics and Statistics

SP - 157

EP - 164

BT - Number Theory and Related Fields

PB - Springer New York LLC

ER -

Small Representations by Indefinite Ternary Quadratic Forms

Abstract

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All Science Journal Classification (ASJC) codes

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