scholarly journals On a divisor problem related to the Epstein zeta-function, II

2011 ◽  
Vol 131 (9) ◽  
pp. 1734-1742
Author(s):  
Guangshi Lü ◽  
Jie Wu ◽  
Wenguang Zhai
Keyword(s):  
Zeta Function ◽  
Divisor Problem ◽  
Epstein Zeta Function

scholarly journals On a divisor problem related to the Epstein zeta-function, IV

2012 ◽  
Vol 154 (3) ◽  
pp. 307-324
Author(s):  
Guangshi Lü ◽  
Jie Wu ◽  
Wenguang Zhai
Keyword(s):  
Zeta Function ◽  
Divisor Problem ◽  
Epstein Zeta Function

scholarly journals Minimal theta functions

1988 ◽  
Vol 30 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Hugh L. Montgomery
Keyword(s):  
Functional Equation ◽  
Quadratic Form ◽  
Zeta Function ◽  
Theta Functions ◽  
Binary Quadratic Form ◽  
Positive Definite ◽  
Epstein Zeta Function ◽  
Image Position

Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1.Among such forms, let . The Epstein zeta function of f is denned to beRankin [7], Cassels [1], Ennola [5], and Diananda [4] between them proved that for every real s > 0,We prove a corresponding result for theta functions. For real α > 0, letThis function satisfies the functional equation(This may be proved by using the formula (4) below, and then twice applying the identity (8).)

scholarly journals On some mean value results for the zeta-function and a divisor problem II

2015 ◽  
Vol 26 (5) ◽  
pp. 842-866 ◽  
Author(s):  
Aleksandar Ivić ◽  
Wenguang Zhai
Keyword(s):  
Zeta Function ◽  
Mean Value ◽  
Divisor Problem
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