# Tagged Questions

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### An integral representation of the Riemann zeta function

I am referring to the equality in equation $3.29$ (page 12) and $4.20$ (page 17) in this paper. I am unable to recognize where this comes from or what is the general expression for values other than ...
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### Derivative of a function related to Dedekind zeta function

Lef $K$ be an algebraic number field of degree $[K:\mathbb{Q}]=n$. For simplicity suppose $K$ is totally real. Define $f(s) = \zeta_K(s) \zeta(1-s)^{n-1}$ where $\zeta = \zeta_{\mathbb{Q}}$. From the ...
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### Inequalities in paper by Jean Bourgain

The question refers to the following paper by Jean Bourgain: http://arxiv.org/abs/math-ph/0011053 Specifically, I can't derive the following inequality in (1.20): ...
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### How to do such a partitioning?

Assume: $$P \subseteq \{1,2,\dots,N\},\quad |P| = K, \qquad x \in \mathbb{R}_+^K , \qquad w = e^{-j\frac{2\pi}N}$$ and, $$f(l) = \sum_{i=1}^K \sum_{j=1}^K x_i x_j w^{(p_i-p_j)l}$$ I am going to ...
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### The Riemann Hypothesis and the Langlands program

On page 263 of this book review appears the following: Given the centrality of L-functions to the Langlands program, nothing would seem more natural (than a presentation of elementary algebraic ...
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### Are there formulas for the derivatives $\zeta_{F}^{(n)}(0)$ of Dedekind zeta functions?

Let $F/\mathbb{Q}$ be a number field. I'm interested in knowing if there are formulas for the values of the derivatives $\zeta_{F}^{(n)}(0)$ of the Dedekind zeta function of $F$ at zero. Maybe if in ...
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### On meromorphic continuation of zeta function(s) and special values at negative integers

Euler developed (at least) two different approaches in order to calculate the values $\zeta(-m)$ of the zeta function $$\zeta(s) = \sum_{n\geq 1} \frac{1}{n^s}$$ at non-positive integers. In one ...
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### Where Can i find the lecture Videos of BSD 2011

i recently heard that there was a conference on Birch and Swinnerton dyer conjecture Held at Cambridge on May 4 until May 6, the main theme is "The conference marks the 50th anniversary of the ...
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### Why is $\frac{\sqrt{6}}{32}(29 + \sqrt{145}) \approx \pi$ ?

Apologies in advance if this is a stupid question; also, disclaimer: this is purely for fun; but: Why is $\frac{\sqrt{6}}{32}(29 + \sqrt{145})$ such a good approximation to $\pi$? (Correct to 8 ...
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### Class Numbers and 163

This is a bit fluffier of a question than I usually aim for, so apologies in advance if this doesn't pass the smell test for suitability. Likely my favorite fun fact in all of number theory is the ...
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### BSD conjecture and L functions with zeroes of order g

If the group of rational points of $E$, which is finitely generated by the Mordell-Weil Theorem, has $g$ generators of infinite order, then the Birch-Swinnerton-Dyer conjecture gives $L_E(s)$ has a ...