scholarly journals Moments of the Riemann zeta function on short intervals of the critical line

2021 ◽  
Vol 49 (6) ◽  
Author(s):  
Louis-Pierre Arguin ◽  
Frédéric Ouimet ◽  
Maksym Radziwiłł
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Critical Line ◽  
Short Intervals ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

2018 ◽  
Vol 72 (3) ◽  
pp. 500-535 ◽  
Author(s):  
Louis-Pierre Arguin ◽  
David Belius ◽  
Paul Bourgade ◽  
Maksym Radziwiłł ◽  
Kannan Soundararajan
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Critical Line ◽  
Short Interval ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Small values of the Riemann zeta function on the critical line

2015 ◽  
Vol 169 (3) ◽  
pp. 201-220 ◽  
Author(s):  
Justas Kalpokas ◽  
Paulius Šarka
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Critical Line ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Null trajectories for the symmetrized Hurwitz zeta function

2006 ◽  
Vol 463 (2077) ◽  
pp. 303-319 ◽  
Author(s):  
Ross C McPhedran ◽  
Lindsay C Botten ◽  
Nicolae-Alexandru P Nicorovici
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Critical Line ◽  
Hurwitz Zeta Function ◽  
Trigonometric Functions ◽  
Asymptotic Results ◽  
End Points ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Pass Through

We consider the Hurwitz zeta function ζ ( s , a ) and develop asymptotic results for a = p / q , with q large, and, in particular, for p / q tending to 1/2. We also study the properties of lines along which the symmetrized parts of ζ ( s , a ), ζ + ( s , a ) and ζ − ( s , a ) are zero. We find that these lines may be grouped into four families, with the start and end points for each family being simply characterized. At values of a =1/2, 2/3 and 3/4, the curves pass through points which may also be characterized, in terms of zeros of the Riemann zeta function, or the Dirichlet functions L −3 ( s ) and L −4 ( s ), or of simple trigonometric functions. Consideration of these trajectories enables us to relate the densities of zeros of L −3 ( s ) and L −4 ( s ) to that of ζ ( s ) on the critical line.

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