scholarly journals On the asymptotically uniform distribution of the zeros of the partial sums of the Riemann zeta function

2013 ◽  
Vol 403 (1) ◽  
pp. 120-128 ◽  
Author(s):  
G. Mora
Keyword(s):  
Zeta Function ◽  
Uniform Distribution ◽  
Riemann Zeta Function ◽  
Partial Sums ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals On The Tails of the Exponential Series

1994 ◽  
Vol 37 (2) ◽  
pp. 278-286 ◽  
Author(s):  
C. Yalçin Yildirim
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Partial Sums ◽  
Maclaurin Series ◽  
Exponential Series ◽  
Asymptotic Estimation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

AbstractA relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.

scholarly journals Applications of uniform distribution theory to the Riemann zeta-function

2015 ◽  
Vol 64 (1) ◽  
pp. 67-74
Author(s):  
Selin Selen Özbek ◽  
Jörn Steuding
Keyword(s):  
Zeta Function ◽  
Uniform Distribution ◽  
Half Plane ◽  
Riemann Zeta Function ◽  
Distribution Theory ◽  
The Riemann Zeta Function ◽  
Upper Half Plane ◽  
Riemann Zeta ◽  
Positive Integers

Abstract We give two applications of uniform distribution theory to the Riemann zeta-function. We show that the values of the argument of are uniformly distributed modulo , where P(n) denotes the values of a polynomial with real coefficients evaluated at the positive integers. Moreover, we study the distribution of arg modulo π, where γn is the nth ordinate of a zeta zero in the upper half-plane (in ascending order).

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