On the mean value of generalized Dirichlet $${\varvec{L}}$$-functions with weight of the character sums

2021 ◽  
Vol 131 (2) ◽  
Author(s):  
Rong Ma ◽  
Yana Niu ◽  
Haodong Wang ◽  
Yulong Zhang
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
The Mean ◽  
Generalized Dirichlet

scholarly journals On the mean value of the generalized Dirichlet L-functions

2010 ◽  
Vol 60 (3) ◽  
pp. 597-620 ◽  
Author(s):  
Rong Ma ◽  
Yuan Yi ◽  
Yulong Zhang
Keyword(s):  
Mean Value ◽  
The Mean ◽  
Generalized Dirichlet

scholarly journals The mean value of the generalized Dirichlet L-functions with the weight of the Gauss sums

2021 ◽  
pp. 1-18
Author(s):  
Yana Niu ◽  
Rong Ma ◽  
Yulong Zhang ◽  
Peilin Jiang
Keyword(s):  
Asymptotic Formula ◽  
Real Number ◽  
Analytic Continuation ◽  
Dirichlet Character ◽  
Mean Value ◽  
Gauss Sums ◽  
Number Formula ◽  
Sum Formula ◽  
The Mean ◽  
Generalized Dirichlet

Let [Formula: see text] be an integer, and let [Formula: see text] denote a Dirichlet character modulo [Formula: see text]. For any real number [Formula: see text], we define the generalized Dirichlet [Formula: see text]-function as [Formula: see text] where [Formula: see text] with [Formula: see text] and [Formula: see text] both real. It can be extended to all [Formula: see text] using analytic continuation. For any integer [Formula: see text], the famous Gauss sum [Formula: see text] is defined as [Formula: see text] where [Formula: see text]. This paper uses analytic methods to study the mean value properties of the generalized Dirichlet [Formula: see text]-functions with the weight of the Gauss sums, and a sharp asymptotic formula is obtained.

scholarly journals Mean Value of the General Dedekind Sums over Interval \({[1,\frac{q}{p})}\)

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2079
Author(s):  
Lei Liu ◽  
Zhefeng Xu
Keyword(s):  
Character Sums ◽  
Mean Value ◽  
Dedekind Sums ◽  
Hybrid Mean Value ◽  
Asymptotic Formulae ◽  
The Mean

Let q>2 be a prime, p be a given prime with p<q. The main purpose of this paper is using transforms, the hybrid mean value of Dirichlet L-functions with character sums and the related properties of character sums to study the mean value of the general Dedekind sums over interval [1,qp), and give some interesting asymptotic formulae.

scholarly journals On asymptotic properties of the generalized Dirichlet L-functions

2019 ◽  
Vol 15 (06) ◽  
pp. 1305-1321
Author(s):  
Rong Ma ◽  
Yana Niu ◽  
Yulong Zhang
Keyword(s):  
Real Number ◽  
Analytic Continuation ◽  
Asymptotic Properties ◽  
Dirichlet Character ◽  
Mean Value ◽  
Analytic Method ◽  
Asymptotic Formulae ◽  
Number Formula ◽  
The Mean ◽  
Generalized Dirichlet

Let [Formula: see text] be an integer, [Formula: see text] denote a Dirichlet character modulo [Formula: see text], for any real number [Formula: see text], we define the generalized Dirichlet [Formula: see text]-functions [Formula: see text] where [Formula: see text] with [Formula: see text] and [Formula: see text] both real. It can be extended to all [Formula: see text] by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet [Formula: see text]-functions, and obtain several sharp asymptotic formulae by using analytic method.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

Detection of Soluble Fibrin Monomer Complexes in Blood by Means of Protamine Sulphate Test

1968 ◽  
Vol 20 (01/02) ◽  
pp. 044-049 ◽  
Author(s):  
B Lipiński ◽  
K Worowski
Keyword(s):  
Human Subjects ◽  
Coronary Thrombosis ◽  
Mean Value ◽  
Healthy Human ◽  
Protamine Sulphate ◽  
Soluble Fibrin ◽  
Fibrin Monomer ◽  
Dog Plasma ◽  
The Mean ◽  
Precipitable Protein

SummaryIn the present paper described is a simple test for detecting soluble fibrin monomer complexes (SFMC) in blood. The test consists in mixing 1% protamine sulphate with diluted oxalated plasma or serum and reading the optical density at 6190 Å. In experiments with dog plasma, enriched with soluble fibrin complexes, it was shown that OD read in PS test is proportional to the amount of fibrin recovered from the precipitate. It was found that SFMC level in plasma increases in rabbits infused intravenously with thrombin and decreases after injection of plasmin with streptokinase. In both cases PS precipitable protein in serum is elevated indicating enhanced fibrinolysis. In healthy human subjects the mean value of OD readings in plasma and sera were found to be 0.30 and 0.11, while in patients with coronary thrombosis they are 0.64 and 0.05 respectively. The origin of SFMC in circulation under physiological and pathological conditions is discussed.

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