Let 
be a nonprincipal number theoretic character
over 
.
Then for any integer 
,
 |
Pólya-Vinogradov Inequality
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References
Davenport, H. "The Pólya-Vinogradov Inequality." Ch. 23 in Multiplicative Number Theory, 2nd ed. New York: Springer-Verlag, pp. 135-138, 1980.Pólya, G. "Über die Verteilung der quadratischen Reste und Nichtreste." Nachr. Königl. Gesell. Wissensch. Göttingen, Math.-phys. Klasse, 21-29, 1918.Vinogradov. Perm. Univ. Fiz.-Mat. ob.-vo Zh. 1, 18-24 and 94-98, 1918.Referenced on Wolfram|Alpha
Pólya-Vinogradov InequalityCite this as:
Weisstein, Eric W. "Pólya-Vinogradov Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Polya-VinogradovInequality.html