Timeline for L functions of Symmetric power of elliptic curves
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2020 at 21:37 | comment | added | OmniaOperator | I think the convergence is essentially the same, taking about $N$ terms. My reading of the M-W result is the Mellin transform dies like $O(\exp(-x^{2/3}))$ and Zagier's dies like $O(\exp(-\sqrt x))$ (he uses a degree 4 product, rather than the direct degree 3 symmetric square, so his convergence is marginally slower). Here $x=n/N$. | |
| Jul 31, 2020 at 14:22 | comment | added | Dianbin Bao | @OmniaOperator, 4.4 of Martin and Watkins use Cauchy residue theorem to shift contour of integration and it turns out to converge really slow as it is the case of Dirichlet series. The method in Zagier's paper use K-bessel function, which speed up the convergence to exponential decay. | |
| Jul 30, 2020 at 18:40 | comment | added | OmniaOperator | The method for passing from a functional equation to computing (approximating) values is due to Lavrik. See Appendix B of Henri Cohen's second book (Advanced topics in computational number theory). Also useful is Buhler, Schoen, and Top (Cycles, L-functions and triple products of elliptic curves) who do the symmetric cube, and 4.4 of Martin and Watkins (Symmetric powers of elliptic curve L-functions). | |
| Jul 30, 2020 at 17:29 | history | asked | Dianbin Bao | CC BY-SA 4.0 |