The mellin transform of Hardy’s function is entire

2010 ◽  
Vol 88 (3-4) ◽  
pp. 612-616
Author(s):  
M. Jutila
Keyword(s):  
Mellin Transform ◽  
Hardy’S Function

scholarly journals An estimate for the Mellin transform of powers of Hardy's function.

2010 ◽  
Vol Volume 33 ◽  
Author(s):  
Matti Jutila
Keyword(s):  
Entire Function ◽  
Zeta Function ◽  
Mellin Transform ◽  
Critical Line ◽  
Classical Estimate ◽  
International Audience ◽  
Hardy’S Function

International audience We show that a certain modified Mellin transform $\mathcal M(s)$ of Hardy's function is an entire function. There are reasons to connect $\mathcal M(s)$ with the function $\zeta(2s-1/2)$, and then the orders of $\mathcal M(s)$ and $\zeta(s)$ should be comparable on the critical line. Indeed, an estimate for $\mathcal M(s)$ is proved which in the particular case of the critical line coincides with the classical estimate of the zeta-function.

scholarly journals On the Mellin transforms of powers of Hardy's function.

2010 ◽  
Vol Volume 33 ◽  
Author(s):  
Aleksandar Ivić
Keyword(s):  
Mellin Transform ◽  
Mellin Transforms ◽  
International Audience ◽  
Power Moments ◽  
Hardy’S Function ◽  
Natural Boundaries

International audience Various properties of the Mellin transform function $$\mathcal{M}_k(s):= \int_1^{\infty} Z^k(x)x^{-s}\,dx$$ are investigated, where $$Z(t):=\zeta(\frac{1}{2}+it)\,\chi(\frac{1}{2}+it)^{-1/2},~~~~\zeta(s)=\chi(s)\zeta(1-s)$$ is Hardy's function. Connections with power moments of $|\zeta(\frac{1}{2}+it)|$ are established, and natural boundaries of $\mathcal{M}_k(s)$ are discussed.

scholarly journals A Mellin Transform Approach to the Pricing of Options with Default Risk

2021 ◽  
Author(s):  
Sun-Yong Choi ◽  
Sotheara Veng ◽  
Jeong-Hoon Kim ◽  
Ji-Hun Yoon
Keyword(s):  
Default Risk ◽  
Mellin Transform

g-Mellin transform in probability theory

2020 ◽  
Author(s):  
Teodora Gavrilov ◽  
Natasa Durakovic ◽  
Katarina Gavrilov ◽  
Tatjana Grbic ◽  
Slavica Medic ◽  
...  
Keyword(s):  
Probability Theory ◽  
Mellin Transform

Analytical solution of the PELDOR inverse problem using the integral Mellin transform

2017 ◽  
Vol 19 (48) ◽  
pp. 32381-32388 ◽  
Author(s):  
Anna G. Matveeva ◽  
Vyacheslav M. Nekrasov ◽  
Alexander G. Maryasov
Keyword(s):  
Inverse Problem ◽  
Distribution Function ◽  
Analytical Solution ◽  
Short Distance ◽  
Mellin Transform ◽  
Distance Distribution ◽  
Distance Distribution Function ◽  
Distance Range ◽  
Model Free ◽  
Model Free Approach

The model-free approach used does not introduce systematic distortions in the computed distance distribution function between two spins and appears to result in noise grouping in the short distance range.

THE NLO QCD CALCULATION OF SEA QUARK DISTRIBUTIONS IN THE CORGI APPROACH, BASED ON THE CONSTITUENT QUARK MODEL

2007 ◽  
Vol 22 (24) ◽  
pp. 4519-4535 ◽  
Author(s):  
A. MIRJALILI ◽  
K. KESHAVARZIAN
Keyword(s):  
Quark Model ◽  
Mellin Transform ◽  
Constituent Quark ◽  
Constituent Quark Model ◽  
Standard Approach ◽  
Unknown Parameters ◽  
Electron Positron Annihilation ◽  
Electron Positron ◽  
Physical Scale ◽  
Good Agreement

Sea quark distributions in the NLO approximation, based on the phenomenological valon model or constituent quark model are analyzed. We use the parametrized inverse Mellin transform technique to perform a direct fit with available experimental data and obtain the unknown parameters of the distributions. We try to extend the calculation to the NLO approximation for the singlet and nonsinglet cases in DIS phenomena. We do also the same calculation for electron–positron annihilation. The resulting sea distributions are effectively independent of the process used. The approach of complete RG improvement (CORGI) is employed and the results are compared with the standard approach of perturbative QCD in the [Formula: see text] scheme with a physical scale. The comparisons with data are in good agreement. As is expected, the results in the CORGI approach indicate a better agreement to the data than the NLO calculation in the standard approach.

scholarly journals On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields

1971 ◽  
Vol 43 ◽  
pp. 199-208 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Elliptic Curves ◽  
Cusp Form ◽  
Mellin Transform ◽  
Quadratic Field ◽  
Congruence Subgroup ◽  
Function Fields ◽  
Complex Multiplication ◽  
Modular Function ◽  
Imaginary Quadratic Field

1. As Hecke showed, every L-function of an imaginary quadratic field K with a Grössen-character γ is the Mellin transform of a cusp form f(z) belonging to a certain congruence subgroup Γ of SL2(Z). We can normalize γ so that

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