https://github.com/davidayotte/sym2-dihedral
This repo contains functions about dihedral congruence for modular forms and computations on the trace of the symmetric square L function
https://github.com/davidayotte/sym2-dihedral
bernoulli-number dihedral-congruence modular-forms symmetric-square-l-function
Last synced: 4 months ago
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This repo contains functions about dihedral congruence for modular forms and computations on the trace of the symmetric square L function
- Host: GitHub
- URL: https://github.com/davidayotte/sym2-dihedral
- Owner: DavidAyotte
- License: mit
- Created: 2019-06-04T19:45:01.000Z (about 7 years ago)
- Default Branch: master
- Last Pushed: 2021-05-12T16:01:21.000Z (about 5 years ago)
- Last Synced: 2025-06-11T10:57:24.430Z (12 months ago)
- Topics: bernoulli-number, dihedral-congruence, modular-forms, symmetric-square-l-function
- Language: Gnuplot
- Homepage:
- Size: 15.6 KB
- Stars: 1
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Sym2-Dihedral
This repo contains multiple functions written in PARI/GP about modulars forms, Bernoulli numbers and L-functions. More precisely, on the trace of the symmetric-square L-function and dihedral congruences of modular forms. This code was written as part of my master thesis.
## Files
* `trace.gp`: functions about the trace of the Symmetric square L-function as defined by Dummigan and Heim
* `dihedral.gp`: functions about dihedral congruences on modular forms
* `misc.gp`: miscellaneous functions about p-valuation of Bernoulli numbers and modular forms
In a gp session, after reading a file, you can type `? name_of_file` to obtain more information about the file.
## References
* Ayotte, D, Relations entre le nombre de classes et les formes modulaires, master thesis (2019)
* Dummigan, Neil; Heim, Bernhard, Symmetric square L-values and dihedral congruences for cusp forms. J. Number Theory 130 (2010)
* Brown, Alexander F.; Ghate, Eknath P. Dihedral congruence primes and class fields of real quadratic fields. J. Number Theory 95 (2002)