Timeline for Adelic Schwartz class
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2017 at 22:11 | vote | accept | john mangual | ||
| Apr 7, 2017 at 20:08 | comment | added | LSpice | A very literal answer to the request for a book on $\mathrm{GL}_2$ is ams.org/mathscinet-getitem?mr=401654 (SLN 114). If you're willing to go up to $\mathrm{GL}_3$, Bump may be more friendly ams.org/mathscinet-getitem?mr=765698 (SLN 1083). For $\mathrm{GL}_2$ again, I like the book of Bushnell and Henniart ams.org/mathscinet-getitem?mr=2234120 , but it's local. | |
| Apr 7, 2017 at 18:47 | history | edited | Abdelmalek Abdesselam | CC BY-SA 3.0 |
edited title
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| Apr 7, 2017 at 16:35 | comment | added | Peter Humphries | Don't get ahead of yourself. A Bruhat-Schwartz function is a finite linear combination of these pure tensors. What is a $\mathrm{SL}_2(\mathbb{Z})$ average of a function on $\mathbb{A}$? Seriously, read Goldfeld and Hundley. It explains the dictionary between classical and adèlic automorphic forms. | |
| Apr 7, 2017 at 16:31 | comment | added | john mangual | I think about it some more if I have these monomial elements of Schwartz class, then I can put arbitrary linear combinations of these things and still remain in Schwartz class or add $\mathbb{Z}$-averages (or $SL(2, \mathbb{Z})$ averages?) In any case $\theta$ functions and other automorphic functions, hopefully remain in this safety class. | |
| Apr 7, 2017 at 15:14 | comment | added | john mangual | @PeterHumphries that is what I need a whole book on $GL_2$ and all it's variants $GL_2(\mathbb{A})$ and $GL_2(\mathbb{Q}_p)$. | |
| Apr 7, 2017 at 15:11 | comment | added | Peter Humphries | Those notes are not the place to learn automorphic representations for the first time. | |
| Apr 7, 2017 at 15:10 | comment | added | john mangual | I found these lecture notes of Ngô, $p$-adic representation theory is a whole topic in itself, and here they write it in a few sentences. | |
| Apr 7, 2017 at 14:54 | answer | added | Abdelmalek Abdesselam | timeline score: 2 | |
| Apr 7, 2017 at 14:50 | comment | added | Peter Humphries | Read chapter 1 of Goldfeld and Hundley. Anyway, the $p$-adic component of a Bruhat-Schwartz function is a locally constant compactly supported function, and is the indicator function of $\mathcal{O}_v$ for all but finitely many nonarchimedean places $v$. | |
| Apr 7, 2017 at 14:27 | history | asked | john mangual | CC BY-SA 3.0 |