Distribution of values of L
-functions at the edge of the critical strip

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .

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The Distribution of Values of the Riemann Zeta Function, I

An Introduction to Probabilistic Number Theory ◽

10.1017/9781108888226.004 ◽

2021 ◽

pp. 47-74

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Distribution Of Values ◽

The Riemann Zeta Function ◽

Riemann Zeta

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Effective Estimates for the Distribution of Values of Euler Products

Monatshefte für Mathematik ◽

10.1007/s00605-005-0305-4 ◽

2005 ◽

Vol 145 (2) ◽

pp. 97-106 ◽

Cited By ~ 1

Author(s):

Ernesto Girondo ◽

Jörn Steuding

Keyword(s):

Distribution Of Values ◽

Euler Products

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Neural network processing of radar scanning data array

Neurocomputers ◽

10.18127/j19998554-202104-02 ◽

2021 ◽

Author(s):

V.E. Dmitriyev ◽

D.V. Popov ◽

V.A. Shakhnov

Keyword(s):

Spatial Perception ◽

Digital Processing ◽

Radar Data ◽

Information Value ◽

Data Array ◽

Additional Information ◽

Distribution Of Values ◽

The Difference ◽

Radar Data Processing ◽

Made In

This article deals with the digital processing of a matrix radar image. The information received from the radar scanner needs to be transformed to enable visual perception. The article describes the main methods of digital processing of matrix data, presents the images transformed by them. The aim of the article was the development of a radar data processing algorithm that identifies the contours and edges of examined objects. The authors propose an algorithm for isolating the geometric structure of the scanned area. The difference between the processing method and the known analogues is based on the nature of the change in the values of the array being processed and consists in the double operation of extracting the gradient of the distribution of values. The software implementation of the algorithm is made in C++ using methods from an open library of computer vision. The efficiency of the algorithm was estimated based on comparison with the algorithms for determining edges based on linear filtering and neural networks. The results of the work can be used to create software for mobile short-range radar devices. Imaging from object boundaries and their edges provides spatial perception of the image by the operator, and free areas are available for rendering additional information. This solution allows you to combine scanning devices and thereby increase the information value of the result.

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Nonvanishing of derivatives of Hecke $$L$$L-functions associated to cusp forms inside the critical strip

The Ramanujan Journal ◽

10.1007/s11139-018-0073-0 ◽

2018 ◽

Vol 51 (2) ◽

pp. 319-327

Author(s):

Winfried Kohnen ◽

Jyoti Sengupta ◽

Miriam Weigel

Keyword(s):

Cusp Forms ◽

Critical Strip ◽

Derivatives Of

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Distribution of values of classic singular Cantor function of random argument

Random Operators and Stochastic Equations ◽

10.1515/rose-2018-0016 ◽

2018 ◽

Vol 26 (4) ◽

pp. 193-200 ◽

Cited By ~ 1

Author(s):

Mykola Pratsiovytyi ◽

Iryna Lysenko ◽

Oksana Voitovska

Keyword(s):

Random Variable ◽

Absolutely Continuous ◽

Cantor Function ◽

Distribution Of Values

Abstract Let X be a random variable with independent ternary digits and let {y=F(x)} be a classic singular Cantor function. For the distribution of the random variable {Y=F(X)} , the Lebesgue structure (i.e., the content of discrete, absolutely continuous and singular components), the structure of its point and the continuous spectra are exhaustively studied.

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