#12724: Allow different normalizations for Eisenstein series q-expansion
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Reporter: davidloeffler | Owner: craigcitro
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: modular forms | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: David Loeffler | Merged in:
Dependencies: | Stopgaps:
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Description changed by davidloeffler:
Old description:
> This came up as part of my review of #12043, but it's of independent
> interest.
>
> The level 1 Eisenstein series can be normalized in three natural ways: so
> the linear term is 1; so the constant term is 1; or so the coefficients
> are integers with no common factor. Renormalizing is no problem if you're
> working over QQ but over finite characteristic base rings it is a total
> pain (try computing E_p-1_ mod p^2^).
>
> The patch below modifies {{{ eisenstein_series_qexp }}} so the following
> works:
> {{{
> sage: eisenstein_series_qexp(6, 5, normalization="constant")
> 1 - 504*q - 16632*q^2 - 122976*q^3 - 532728*q^4 + O(q^5)
> sage: eisenstein_series_qexp(6, 10, K=Zmod(49), normalization="constant")
> 1 + 35*q + 28*q^2 + 14*q^3 + 42*q^5 + 21*q^6 + 35*q^7 + 35*q^8 + 7*q^9 +
> O(q^10)
> }}}
New description:
This came up as part of my review of #12043, but it's of independent
interest.
The level 1 Eisenstein series can be normalized in three natural ways: so
the linear coefficient is 1; so the constant term is 1; or so the
coefficients are integers with no common factor. Renormalizing is no
problem if you're working over QQ but over finite characteristic base
rings it is a total pain (try computing E,,p-1,, mod p^2^).
The patch below modifies {{{ eisenstein_series_qexp }}} so the following
works:
{{{
sage: eisenstein_series_qexp(6, 5, normalization="constant")
1 - 504*q - 16632*q^2 - 122976*q^3 - 532728*q^4 + O(q^5)
sage: eisenstein_series_qexp(6, 10, K=Zmod(49), normalization="constant")
1 + 35*q + 28*q^2 + 14*q^3 + 42*q^5 + 21*q^6 + 35*q^7 + 35*q^8 + 7*q^9 +
O(q^10)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12724#comment:2>
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