Premium
The distribution of quadratic residues and non‐residues
Author(s) -
Burgess D. A.
Publication year - 1957
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300001157
Subject(s) - mathematics , citation , distribution (mathematics) , quadratic residue , quadratic equation , library science , combinatorics , mathematics education , information retrieval , computer science , mathematical analysis , geometry
If p is a prime other than 2, half of the numbers 1, 2, … p —1 are quadratic residues (mod p ) and the other half are quadratic non-residues. Various questions have been proposed concerning the distribution of the quadratic residues and non-residues for large p , but as yet only very incomplete answers to these questions are known. Many of the known results are deductions from the inequality found independently by Polya and Vinogradov, the symbol being Legendre's symbol of quadratic character.