scholarly journals OPPOSITE‐SIGN KLOOSTERMAN SUM ZETA FUNCTION

Mathematika ◽  
2016 ◽  
Vol 62 (2) ◽  
pp. 406-429 ◽  
Author(s):  
Eren Mehmet Kıral
Keyword(s):  
Zeta Function ◽  
Opposite Sign ◽  
Kloosterman Sum

scholarly journals Divergent Integrals, The Riemann Zeta Function, and The Vacuum

2020 ◽  
Author(s):  
Siamak Tafazoli
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Vacuum Energy ◽  
Opposite Sign ◽  
Vacuum Energy Density ◽  
Power Functions ◽  
Vacuum States ◽  
The Riemann Zeta Function ◽  
Order Of Magnitude ◽  
Riemann Zeta

This paper presents a new estimate for the vacuum energy density by summing the contributions of all quantum fields' vacuum states which turns out to be in the same order of magnitude (but with opposite sign) as the predictions of current cosmological models and all observational data to date. The basis for this estimate is the recent results on the analytical solution to improper integral of divergent power functions using the Riemann Zeta function.

Pb Electrodeposition in the Presence of Chlorine Ions on Cu(100): An in Situ Optical Reflectivity Difference Study

2003 ◽  
Vol 781 ◽  
Author(s):  
J. Gray ◽  
W. Schwarzacher ◽  
X.D. Zhu
Keyword(s):  
Oblique Incidence ◽  
Opposite Sign ◽  
Bulk Phase ◽  
Phase Layer ◽  
Optical Reflectivity ◽  
Scan Rate ◽  
Different Types ◽  
Chlorine Ions ◽  
High Overpotentials

AbstractWe studied the initial stages of the electrodeposition of Pb in the presence of chlorine ions on Cu(100), using an oblique-incidence optical reflectivity difference (OIRD) technique. The OI-RD results reveal that immediately following the underpotential deposition (UPD) of the first Pb monolayer, two different types of bulk-phase films grow depending upon the magnitude of overpotential and cyclic voltammetry (CV) scan rate. At low overpotentials and/or slow scan rates, we propose that a bulk-phase Pb film grows on top of the UPD monolayer. At high overpotentials and/or fast scan rates, either a PbO, PbCl2, or a rough Pb bulk-phase layer grows on top of the UPD layer such that the reflectivity difference signal from such a film has an opposite sign.

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta

Investigation of the Accuracy of Reference Instruments for Measuring Vertical Angles by Reference Method of Their Calibration

2020 ◽  
pp. 3-14
Author(s):  
O. M. Samoylenko ◽  
O. V. Adamenko ◽  
B. P. Kukareka
Keyword(s):  
Horizontal Plane ◽  
Opposite Sign ◽  
Reference Method ◽  
Angle Measurement ◽  
Measurement Standard ◽  
Vertical Angle ◽  
Measurement Standards ◽  
Measurement Results ◽  
Electronic Measurement ◽  
Systematic Biases

Reference method for simultaneous calibration of the three and more measurement standards for vertical angle measurement is developed. This method can to use for obtaining the systematic biases of the vertical angles measurements for each of the measuring standards relative of the horizontal plain was averaged from measurement results in time their calibration or comparison. For realization of the reference method was developed the autocollimationel electronic measurement standard for the automatization measurement of the vertical angles SeaLineZero_Standard™ (SLZ_S™). Summary standard deviation (k=1) of the vertical angle measurement relative the horizontal plane, from the results of their calibration by reference method, is not more 0,07ʺ…0,15ʺ. This result was obtained without the use the systematic biases, for each measurement standards, as measurements corrections (with opposite sign). The measuring standards, that were developed and researched, are necessary for obtaining the systematic biases of the vertical angle measurement for total stations and theodolites, that have the normed standard error 0,5ʺ and 1ʺ, when these instruments are calibrating.

The (α, β)-ramification invariants of a number field

2021 ◽  
Vol 71 (1) ◽  
pp. 251-263
Author(s):  
Guillermo Mantilla-Soler
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Residue Class ◽  
Interesting Application ◽  
Dedekind Zeta Function ◽  
Arithmetic Properties

Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.

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