[2] E.C. Titchmarsh, The Theory of the Riemann Zeta Function. [3] P.G. Rooney, Another proof of the functional equation for the Riemann zeta function. Another Proof of the Functional Equation for the Riemann Zeta Functionwww.sciencedirect.com/science/article/pii/S0022247X84712443编辑...
(1) Titchmarsh points out in his book on the zeta function (section 2.3) that if you blindly apply the Poisson summation formula to the function f(s)=|x|^s, you get the functional equation of the Riemann zeta function immediately, and gives a reference to a paper of Mordell where this...
In this paper we show that if X is a smooth projective scheme, then its F 1-zeta function satisfies the functional equation ζ X ( n s ) = ( 1 ) χζ X ( s ). We further show that the F 1-zeta function ζ G ( s ) of a split reductive group scheme G of rank r with N...
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A symmetrical form of this functional equation is given by (14) (Ayoub 1974), which was proved by Riemann for all complex (Riemann 1859). As defined above, the zeta function with a complex number is defined for . However, has a unique analytic continuation to the entire complex plane...
A Milnor-Thurston type dynamical zeta function ζ L ( Z ) is associated with a family of maps of the interval (1, 1). Changing the direction of time produces a new zeta function ζ′ L ( Z ). These zeta functions satisfy a functional equation ζ L ( Z ) ζ′ L ( εZ )= ζ...
RiemannZetaFunctionBentE.PetersenJanuary23,1996ContentsIntroduction...1TheZetaFunction...2TheFunctionalEquation...6TheZerosoftheZetaFunction...7StieltjesandHadamard...9OddsandEnds.EulerRelation...11Bibliography...12IntroductionThenotesontheRiemannzetafunctionreproducedbelowareinformallecturenotesfromtwolectures...
06 Chill out with this nice differential equation【冷静下来,用这个漂亮的微分方程】 05:31 A Top G Integral【一个顶G积分】 09:25 Integrating the fractional part of a logarithm function【对对数函数的小数部分进行积分】 09:51 My take on this on wonderful infinite series【我对精彩无限系列的看法】...
The Hurwitz zeta function can also be given by the functional equation (6) (Apostol 1995, Miller and Adamchik 1999), or the integral (7) If and , then (8) (Hurwitz 1882; Whittaker and Watson 1990, pp. 268-269). The Hurwitz zeta function satisfies (9) for (Apostol 1995...