Timeline for Fourier relationship between primes and zeros of L functions
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2020 at 5:22 | vote | accept | Shun | ||
| Aug 28, 2020 at 4:59 | comment | added | Peter Humphries | I expect so (though just over $\mathbb{Q}$). | |
| Aug 27, 2020 at 23:28 | comment | added | paul garrett | Isn't some form of the general case in the Iwaniec-Kowalski book on Analytic Number Theory? | |
| Aug 27, 2020 at 22:43 | comment | added | Peter Humphries | I'm not sure if it's written down anywhere, but the proof goes through unchanged, since all that is required is a functional equation, an Euler product, and control on the growth of the $L$-function (which follows from Stirling's formula and the Phragmen-Lindelof convexity principle). | |
| Aug 27, 2020 at 22:10 | comment | added | Shun | @PeterHumphries: Thanks! Can you point to a reference? | |
| Aug 26, 2020 at 10:20 | comment | added | Peter Humphries | This explicit formula can be generalised to hold for any $L$-function of an automorphic representation over $\mathrm{GL}_n(\mathbb{A}_F)$ for a number field $F$. | |
| Aug 26, 2020 at 5:29 | comment | added | Shun | thanks for the link! This answers question (1), in fact for zeta functions of arbitrary number fields and Hecke characters. Do you know of any higher-dimensional generalizations, my question (2)? | |
| Aug 26, 2020 at 5:10 | review | First posts | |||
| Aug 26, 2020 at 8:29 | |||||
| Aug 26, 2020 at 5:01 | history | answered | anon | CC BY-SA 4.0 |