#12724: Allow different normalizations for Eisenstein series q-expansion
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Reporter: davidloeffler | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: modular forms | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: David Loeffler
Merged in: | Dependencies:
Stopgaps: |
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This came up as part of my review of #12046, 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)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12724>
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