Counting Quadratic Nonresidues in Shifted Subsets of the Set of Quadratic Nonresidues for Primes<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>

Rocío Meza-Moreno, Mario Pineda-Ruelas

Type: Article

Publication Date: 2015-01-01

Citations: 1

DOI: https://doi.org/10.1155/2015/163092

Abstract

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>be a prime number and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>the finite field with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>elements. For<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mfenced open="⟦" close="⟧" separators="|"><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mfenced></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>will denote the set of quadratic nonresidues less than or equal to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:math>. In this work we calculate the number of quadratic nonresidues in the shifted set<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mrow></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>a</mml:mi></mml:math>.

Locations

International Journal of Mathematics and Mathematical Sciences - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Counting certain quadratic partitions of zero modulo a prime number	2021	Wang Xiao Aihua Li
+ PDF Chat	On quadratic residues and nonresidues in difference sets modulo 𝑚	1994	J. Fabrykowski
+ PDF Chat	A table of quintic number fields	1994	Albert Schwarz Michael Pohst Fredéric Diaz
+	The least quadratic non-residue	2021	Kevin J. McGown Enrique Treviño
+ PDF Chat	Quadratic fields with special class groups	1992	James J. Solderitsch
+	Exponents of class groups of real quadratic function fields	2004	Kalyan Chakraborty Anirban Mukhopadhyay
+	Comparison of 4-class ranks of certain quadratic fields	2001	Frank Gerth
+ PDF Chat	A note on class-number one in certain real quadratic and pure cubic fields	1986	M. Tennenhouse H. C. Williams
+ PDF Chat	On the distribution of quadratic residues and nonresidues modulo a prime number	1992	René Peralta
+	Exploring the Proportion of Prime Numbers in Quadratic Extensions of the Integers	2018	Jamie Lindemann Nelson
+ PDF Chat	Non-primitive number fields of degree eight and of signature (2,3), (4,2), and (6,1) with small discriminant	1999	Schehrazad Selmane
+ PDF Chat	The class number of 𝑄(√-𝑝), for 𝑃≡1(𝑚𝑜𝑑8) a prime	1972	Ezra Brown
+ PDF Chat	Class groups of the quadratic fields found by F. Diaz y Diaz	1976	Daniel Shanks
+	Quadratic extensions of the integers, ℤ[√𝕕]	2018
+ PDF Chat	On quadratic Waring’s problem in totally real number fields	2022	Jakub Krásenský Pavlo Yatsyna
+ PDF Chat	Quadratic polynomials which have a high density of prime values	1990	Gilbert Fung Hywel C Williams
+ PDF Chat	Enumeration of quartic fields of small discriminant	1993	Johannes Buchmann David Ford Michael Pohst
+ PDF Chat	Class groups of quadratic fields	1976	Duncan A. Buell
+ PDF Chat	Distinguished representations and quadratic base change for 𝐺𝐿(3)	1996	Hervé Jacquet Yangbo Ye
+ PDF Chat	Integer sequences having prescribed quadratic character	1970	D. H. Lehmer Emma Lehmer Daniel Shanks

Works That Cite This (1)

Action	Title	Year	Authors
+	Propiedades aditivas en subconjuntos de los residuos cuadráticos	2015	Rocío Meza Moreno

Works Cited by This (2)

Action	Title	Year	Authors
+	On the Distribution of Powers in Finite Fields	1998	Arne Winterhof
+	Bemerkungen �ber die Verteilung der quadratischen Reste	1952	Oskar Perron