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Nov
13 |
comment |
Do Shintani zeta functions satisfy a functional equation?
@David: The Shintani zeta functions that Frank Thorne studies are the first type $\zeta^{SS}$ that OP mentions. |
Aug
12 |
awarded | Yearling |
Aug
3 |
comment |
Is there a $q$-L'Hospital's Rule?
This limit appears to diverge, and it doesn't match the limit in the Stack Exchange question. Could you please clarify? |
Jan
13 |
answered | Sharp upper bounds on hypergeometric function ${}_2F_1[a,b,c;z]$ when $|z|\geq1$ |
Jan
13 |
revised |
Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$
clarification |
Jan
13 |
revised |
Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$
clarification |
Jan
13 |
answered | Is this combination of generalized polygamma and dilogarithm actually zero? $\Im\;\psi^{(-2)}(1+i)+\frac1{4\pi}\text{Li}_2(e^{-2\pi})-\log\sqrt{2\pi}+\frac{5\pi}{24}+\frac12$ |
Aug
12 |
awarded | Yearling |
Jul
2 |
awarded | Curious |
Nov
13 |
awarded | Good Question |
Nov
5 |
awarded | Popular Question |
Oct
21 |
comment |
Euclidean real quadratic fields
I'm not sure what you mean by "a single (or finitely many) Euclidean function(s)"; how do you tell whether two Euclidean functions for different number rings are the same or different? Anyway, this paper arxiv.org/abs/1106.0856 might interest you. |
Oct
21 |
comment |
Jokes in the sense of Littlewood: examples?
@Michael: I'm not quite sure what you're getting at. The $\lambda_i$ live in $\overline{K(x_{11}, x_{12}, \cdots, x_{nn})}$ but not in $K(x_{11}, x_{12}, \cdots, x_{nn})$, so that doesn't tell you anything downstairs. |
Oct
9 |
comment |
When is a Number Ring generated by its Norm-1 elements?
For a real quadratic field of discriminant $d$, the condition holds if and only if $\frac{d}{4}+1$ is a square, so, as you said, rarely. However, the relationship Bump mentions works for all real quadratic fields, if you phrase it as, "there's a natural bijection between the ideal classes of all orders $\mathcal{O}$ of $K$ and the hyperbolic conjugacy classes of ${\rm PSL}_2(\mathbb{Z})$ with eigenvalues in $K$." Your condition guarantees that the ideals of the max order $\mathcal{O}_K$ correspond to the conjugacy classes having the fundamental unit as an eigenvalue. |
Sep
4 |
revised |
Set of primes dividing polynomials and composition
added 216 characters in body |
Sep
4 |
answered | Set of primes dividing polynomials and composition |
Aug
12 |
awarded | Yearling |
Jul
28 |
comment |
Subgroups of finite index of fields
No. Consider finite fields. |
Jul
25 |
comment |
Class numbers of orders
Updated the answer. Thanks for pointing that out, David. |
Jul
25 |
revised |
Class numbers of orders
added 259 characters in body |