On the role of three functions in the Riemann literatures

In Riemann's paper and Nachlass on the zeta function, $\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ has three different functional expressions, of which $$\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)=2\Re[\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})f(s)],\qquad\Re(s)=1/2$$ still has no literature to study it so far. Based on its geometric meaning, we obtain the number of zeros of the Riemann zeta function on the critical line is $$\frac{T}{2\pi}\log\frac{T}{2\pi}-\frac{T}{2\pi}+\frac{\arg{f(1/2+iT)}}{\pi}+O(T^{-1}).$$ Research shows that Riemann's assertion about ~"One now finds indeed approximate this number of real roots within these limits" comes from this functional expression of $\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ which associated with the Jacobi function. Finally, this paper analyzes the reason why these conclusions are neglected.Comment: AMS-LaTeX v2.2, 11 page

The impact of the Asian Crisis on Australia's primary exports: why it wasn't so bad

This article explores the modest impact of the Asian Crisis on Australia’s primary commodity exports. Simulations using a global general equilibrium model show: (i) as capital flees Asia, investment in Australia increases and the trade deficit grows; (ii) while terms of trade deteriorate in the short run, they improve in the medium run as import demand increases in the crisis countries; (iii) exports of primary commodities expand as the crisis countries try to export more; (iv) more income‐elastic primary commodities fare less well than the income‐inelastic foodstuffs as incomes decline in the crisis countries; (v) Australia’s relatively low dependence on manufactured exports was a buffer as manufactured exports came under heavy pressure from exports from the crisis countries.International Relations/Trade,

Do Government Preferences Matter for Tax Competition?

This paper explores how government preferences a ect the choices of capital tax rates in the presence of tax competition. We develop a model in which governments, di erentiating in their preferences for economic development and regional equality, compete for mobile capital over corporation taxes. The key prediction of the model, borne out in data from OECD countries over the years 1990-2007, is that countries emphasizing more on economic development tend to choose lower level of corporate income tax rates than the counterparts that stressing more on regional equality. Our result contributes to the tax competition literature by advancing a new element, heterogeneous government preferences, as another potential source of asymmetric tax policy responses that is widely observed across countries