trying to use PARI for L-functions of modular forms

[fchapoton]

instead of the Dokchitser scripts

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[fchapoton]

There remains a problem when handling non-cuspidal forms. Help is welcome.

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[fchapoton]

@AurelPage pourquoi est-ce que la reconnaissance automatique des poles ne marche pas ? Je donne à Pari les coefficients de la serie d'Eisenstein E4, et le parametre pole=0. Je croyais que Pari pouvait alors s'occuper de trouver les poles et le developpement de la fonction L completee en le pole ?

[fchapoton]

Doc : https://pari.math.u-bordeaux.fr/dochtml/html-stable/_L_minusfunctions.html

[AurelPage]

The poles cannot be detected automatically. For L-functions where the dual is the complex conjugate, if you provide the location of the poles and they are simple then the residues can be computed automatically.

[fchapoton]

Merci Aurel.

Donc ca viendrait du fait que j'ai pas déclaré astar = 0 ? ou bien astar = 1 ?

je comprends pas ce que ces deux sentinel-values signifient exactement. EDIT: ok, c'est dans la doc, désolé

The doc says :

Finally, if a = a*, we allow a shortcut to describe the frequent situation where L has at most simple pole, at s = k, with residue r a complex scalar: you may then input poles = r. This value r can be set to 0 if unknown and it will be computed.

[edgarcosta]

Seems okay to me.

[fchapoton]

so is this a positive review ?

[edgarcosta]

yup. sorry!