From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

2021 ◽  
Keyword(s):  
Number Theory ◽  
Orthogonal Polynomials ◽  
Operator Theory

Gauss Sums and Orthogonal Polynomials

1997 ◽  
Vol 12 (01) ◽  
pp. 289-294 ◽  
Author(s):  
A. S. Zhedanov
Keyword(s):  
Number Theory ◽  
Weight Function ◽  
Orthogonal Polynomials ◽  
Hermite Polynomials ◽  
Gauss Sums ◽  
Gauss Sum ◽  
The Real ◽  
Root Of Unity ◽  
Szegő Polynomials

It is shown that q-Hermite polynomials for q a root of unity are orthogonal on finite numbers of points of the real axes. The (complex) weight function coincides with a special type of the Gauss sums in number theory. The same Gauss sum plays the role of the weight function for the Stiltjes–Wigert and Rogers–Szegö polynomials leading to the orthogonality on the regular N-gons.

Multiplicative Number Theory I

2006 ◽  
Author(s):  
Hugh L. Montgomery ◽  
Robert C. Vaughan
Keyword(s):  
Number Theory
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