most recent 30 from http://mathoverflow.net 2013-05-25T12:13:58Z http://mathoverflow.net/feeds/user/2902 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/24501/how-to-compute-divdx Yinbang Lin 2010-05-13T13:04:11Z 2010-07-21T06:31:28Z

<p>Let $C$ be an elliptic curve defined by $y^2=(x-e_1)(x-e_2)(x-e_3)$.</p> <p>My question is how to determine the order of the differential $dx$ at infinity, $ord_{\infty}(dx)$.</p>

http://mathoverflow.net/questions/22618/information-hidden-behind-l-functions Yinbang Lin 2010-04-26T16:50:42Z 2010-05-02T18:14:50Z

<p>By this, I mean, for example, arithmetic progression implied by Riemann zeta function. Are there any resources talking about this topic in general?</p> <p>Moreover, Weil's theorem says that the zeta function of a variety is rational, making it possible to compute the zeta function. Are there any versions of L-functions easy for computation? Are the values of equivalent importance at every point? Are there any general strategies for computing values of L-function?</p> <p>Are there any recent papers on the computation of L-functions and arithmetic information implied by values of it?</p>

http://mathoverflow.net/questions/11207/how-does-the-order-of-a-pole-of-a-zeta-function-indicate-any-geometric-informatio Yinbang Lin 2010-01-09T03:09:59Z 2010-02-28T08:50:18Z

<p>Here, I'm primarily concerced about zeta functions of hypersurfaces over fields of finite characteristic. </p> <p>Assume $F_q$ to be a finite field with q elements. Consider the zeta function of the hypersurface defined by $-y_0^2+y_1^2+y_2^2+y_3^2=0$ in $\mathbb{P}^3$.<br /> If $-1$ is a square in $F_q$, the zeta function is </p> <p>$$Z(u)=\frac{1}{(1-uq^2)(1-uq)^2(1-u)}.$$</p> <p>It has a pole of order $2$ at $1/q$. If not, it's </p> <p>$$Z(u)=\frac{1}{(1-uq^2)(1-uq)(1+uq)(1-u)}.$$ </p> <p>It has a pole of order $1$ at $1/q$.</p> <blockquote> <p>How does orders of poles indicate any geometric information?</p> </blockquote>

http://mathoverflow.net/questions/24501/how-to-compute-divdx Yinbang Lin 2010-05-13T16:48:06Z 2010-05-13T16:48:06Z

I'm reading Silverman's book on my own, I can't understand why it can be manipulated this way, and find no one to consult. So I pose it here.