Re: Finding coefficients in linear combination

["Swati, NoFirstName" <S10@email.sc.edu>]

Thank you for your help!

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From: Loïc Grenié <loic.grenie@gmail.com>
Sent: Wednesday, March 13, 2024 12:49:50 PM
To: Swati, NoFirstName <S10@email.sc.edu>
Cc: Ruud H.G. van Tol <rvtol@isolution.nl>; pari-users@pari.math.u-bordeaux.fr <pari-users@pari.math.u-bordeaux.fr>
Subject: Re: Finding coefficients in linear combination

 

On Wed Mar 13th, 2024, at 17:12, Swati, NoFirstName wrote:

Hello,

Thank you for the correction. By \Delta, I mean the Ramanujan Delta function defined as 24^th power of the Dedekind eta function and the T_{17} refers to the integer weight Hecke operator.

     Then using mfcoefs, and matkermod you should be able to find your

  coefficients, sorry I'm too lazy to write the code myself...

        Best,

             Loïc

 

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From: Ruud H.G. van Tol <rvtol@isolution.nl>
Sent: Wednesday, March 13, 2024 12:09 PM
To: Swati, NoFirstName <S10@email.sc.edu>
Subject: Re: Finding coefficients in linear combination

 

[off-list]

On 2024-03-13 16:37, Swati, NoFirstName wrote:
> I am trying to look for an efficient way to compute the coefficients
> a_{i} in the linear combination of  the form
> \Delta^{129} \mid T_{17} \equiv \sum{j = 1}^{i} a_{i} \Delta^{i} \pmod{3}
> using pari/gp.

Maybe you meant:

\Delta^{129} \mid T_{17} \equiv \sum_{j = 1}^{i} a_{i} \Delta^{i} \pmod{3}

(I only added an underscore after sum)


-- Ruud