ZETA functionsWe define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck–Witt group. We show that this enrichment is related to the topology of the real points of a lift. For cell...
Berndt, Levinson, and Montgomery investigated the general case, meanwhile Akatsuka gave sharper estimates for the first derivative of the Riemann zeta function under the truth of the Riemann hypothesis. In this paper, we extend the results of Akatsuka to the second derivative of the Riemann zeta ...
trivial zeros of the derivative of thezeta-function, ζ′ , are to the right of the critical line [14]. There is a quantitative versionof Speiser’s theorem [8] which is the basis for Levinson’s method [7]. In Levinson’s methodthere is a loss caused by the zeros of ζ′ which ...
Let ζ(s) denote the Riemann zeta-function. This thesis is concerned with estimating discrete moments of the form [Special characters omitted.]where [Special characters omitted.]and the sum runs over the non-trivial (complex) zeros ρ = β + γ of ζ(). Here the function () [Special ch...
摘要: The derivative of the Riemann zeta function was computed numerically on several large sets of zeros at large heights. Comparisons to known and conjectured asymptotics are presented.关键词: Riemann Zeta Function at Zeros DOI: 10.48550/arXiv.1105.4312 被引量: 16 ...
In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivat...
derivativegammalogarithmicfunction对数导数 Physics116AWinter2011ThelogarithmicderivativeoftheGammafunctionInthisnote,Iwillsketchsomeofthemainpropertiesofthelogarithmicderivative∗oftheGammafunction.Theformaldefinitionisgivenby:ψ(x)≡ddxlnΓ(x)=Γ′(x)Γ(x),whereΓ′(x)istheordinaryderivativeofΓ(x)with...
These differences can in part be explained by the reduction in polymer zeta potential upon PEC formation. The formation of the PEC is driven by Coulombic interactions between the positively charged groups on the polymer and the negatively charged groups on insulin [75]. Therefore a degree of char...
This is an analogue of a result of Selberg for the Riemann zeta-function. We also prove a mesoscopiccentral limit theorem forP ′P(z) away from the unit circle, and this is an analogue of a result of Lester for zeta.1. I NTRODUCTIONLet ζ(s) be the Riemann zeta-function, and let...
ZetaOfThree Thread Aug 9, 2014 Tags DerivativeFeynmanFeynman lecturesLecturesSecondderivativeUnitUnit vectorVector Replies: 1 Forum:General Math S Derivative of a rotating unit vector I think this is a textbook-style question, if I am wrong, please redirect me to the forum section where I should...