An explicit formula for the fourth power mean of the Riemann zeta-function
Acta Mathematica, 1993 In this important paper the author establishes an explicit formula for \[ I(T,\Delta)= (\Delta\sqrt{\pi})^{-1} \int_{-\infty}^ \infty |\zeta ({\textstyle {1\over 2}}+iT+it)|^ 4 e^{-(t/\Delta)^ 2} dt \qquad ...
Y. Motohashi
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On two-term exponential sums and their mean values
Electronic Research Archive, 2023 The mean value problems of exponential sums play a very important role in the research of analytic number theory, and many famous number theory problems are closely related to them.
Jianghua Li , Zepeng Zhang, Tianyu Pan
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Dirichlet characters of the rational polynomials
AIMS Mathematics, 2022 Denote by $ \chi $ a Dirichlet character modulo $ q\geq 3 $, and $ \overline{a} $ means $ a\cdot\overline{a} \equiv 1 \bmod q $. In this paper, we study Dirichlet characters of the rational polynomials in the form $ \sum\limits^{q}_{a = 1}'\chi(ma ...
Wenjia Guo, Xiaoge Liu, Tianping Zhang
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Exceptional Points of Degeneracy in Periodic Coupled Waveguides and the Interplay of Gain and Radiation Loss: Theoretical and Experimental Demonstration [PDF]
, 2019 We present a novel paradigm for dispersion engineering in coupled transmission lines (CTLs) based on exceptional points of degeneracy (EPDs). We develop a theory for fourth-order EPDs consisting of four Floquet-Bloch eigenmodes coalescing into one ...
Abdelshafy, Ahmed F. +4 more
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The mean fourth power of real character sums [PDF]
Acta Arithmetica, 2002 Summary: Let \(\chi_q\) denotes the real character modulo \(q\) whenever it exists. For \(X\) and \(Y\) large enough, we prove \[ \sum_{|q| \leq X}\biggl| \sum_{n \leq Y} \chi_q(n)\biggr|^4 \ll XY^2 X^\varepsilon \] for any \(\varepsilon>0\) and where the implied constant depends on \(\varepsilon\).
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Weak lensing power spectra for precision cosmology: Multiple-deflection, reduced shear and lensing bias corrections [PDF]
, 2010 It is usually assumed that the ellipticity power spectrum measured in weak lensing observations can be expressed as an integral over the underlying matter power spectrum. This is true at second order in the gravitational potential. We extend the standard
Albrecht +58 more
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e-Prime: Advances in Electrical Engineering, Electronics and Energy, 2021 This research uses computational fluid dynamics (CFD) to perform a two-stage optimization of power output in multiple vertical-axis wind turbines (VAWT) with straight blades.
Wei-Hsin Chen +6 more
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Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes [PDF]
, 2013 We present a numerical study of turbulence and dynamo action in stratified shearing boxes with zero magnetic flux. We assume that the fluid obeys the perfect gas law and has finite (constant) thermal diffusivity.
Bodo, G. +3 more
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Boundary induced non linearities at small Reynolds Numbers [PDF]
, 2006 We investigate the influence of boundary slip velocity in Newtonian fluids at finite Reynolds numbers. Numerical simulations with Lattice Boltzmann method (LBM) and Finite Differences method (FDM) are performed to quantify the effect of heterogeneous ...
Ansumali +31 more
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Muscular and cardiorespiratory parameters of Brazilian professional futsal players: comparison between top national and regional level athletes [PDF]
Motriz: Revista de Educacao Fisica, 2022 Aim: To compare muscular and cardiorespiratory parameters between Brazilian professional futsal athletes from different competitive levels (national versus regional).
Gabriela B. David +6 more
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