MO editors' lounge

Martin Sleziak

12:44 AM

Jun 16, 2023 at 14:59, by Martin Sleziak

new-tag A new tag form-rings.

Jun 16, 2023 at 14:59, by Martin Sleziak

2

Q: Are the following two characterisations of symplectic modules, using the language of form rings, the same?

Page 205 of the book Classical Groups and Algebraic K-Theory defines a symplectic module to be an arbitrary quadratic module $(M,h,q)$ over a form ring $(R,\Lambda)$ with $(J,\varepsilon)$ where $J=\operatorname{id}_R$, $\varepsilon=-1$ and $\Lambda=R$. In particular, this implies that $R$ is com...

deleted-tag THe tag form-rings no longer exists - probably removed by the tag-pruning script: mathoverflow.net/posts/448993/revisions

2

Q: Are the following two characterisations of symplectic modules, using the language of form rings, the same?

Page 205 of the book Classical Groups and Algebraic K-Theory defines a symplectic module to be an arbitrary quadratic module $(M,h,q)$ over a form ring $(R,\Lambda)$ with $(J,\varepsilon)$ where $J=\operatorname{id}_R$, $\varepsilon=-1$ and $\Lambda=R$. In particular, this implies that $R$ is com...

ra.rings-and-algebras modules quadratic-forms

Martin Sleziak

12:59 PM

1

Q: What is the fundamental solution for the backward heat equation?

According to the theorem of Malgrange and Ehrenpreis a fundamental solution exists for any PDE with constant coefficients. But I didn't manage to find in the literature an explicit formula for the backward heat equation $u_t+\Delta u=0$. So what is the formula or does the fundamental solution e...

reference-request ap.analysis-of-pdes elliptic-pde linear-pde heat-equation

Martin Sleziak

6:07 PM

new-tag Two new tags dirichlet and series. The intention was probably to use the tag dirichlet-series.

1

Q: Ramanujan-like series for $1/\pi^m$ and Dirichlet L-values

A rational Ramanujan-like series for $\pi^{-m}$ and character $\chi$ is a series with rational parameters which is of the following form: $$ \sum_{n=0}^{\infty} \left(\prod_{i=0}^{2m} \frac{(s_i )_{n+x}}{(1)_{n+x}} \right) \sum_{k=0}^{m} a_k (n+x)^k z_0^{n+x} = \frac{\sqrt{(-1)^m \chi}}{\pi^m}....

ramanujan series dirichlet

I have edited the tags on that question.

1

Q: Ramanujan-like series for $1/\pi^m$ and Dirichlet L-values

A rational Ramanujan-like series for $\pi^{-m}$ and character $\chi$ is a series with rational parameters which is of the following form: $$ \sum_{n=0}^{\infty} \left(\prod_{i=0}^{2m} \frac{(s_i )_{n+x}}{(1)_{n+x}} \right) \sum_{k=0}^{m} a_k (n+x)^k z_0^{n+x} = \frac{\sqrt{(-1)^m \chi}}{\pi^m}....

dirichlet-series ramanujan

Martin Sleziak

11:38 PM

And now a top-level tag was added, too:

2

Q: Ramanujan-like series for $1/\pi^m$ and Dirichlet L-values

A rational Ramanujan-like series for $\pi^{-m}$ and character $\chi$ is a series with rational parameters which is of the following form: $$ \sum_{n=0}^{\infty} \left(\prod_{i=0}^{2m} \frac{(s_i )_{n+x}}{(1)_{n+x}} \right) \sum_{k=0}^{m} a_k (n+x)^k z_0^{n+x} = \frac{\sqrt{(-1)^m \chi}}{\pi^m}....

nt.number-theory dirichlet-series ramanujan

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