Re: Regarding computing an eta product

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

Thank you so much for the reply. I see where I was making a mistake.

Swati

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From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
Sent: Wednesday, May 29, 2024 3:41 AM
To: pari-users@pari.math.u-bordeaux.fr <pari-users@pari.math.u-bordeaux.fr>
Subject: Re: Regarding computing an eta product

 

On Wed, May 29, 2024 at 03:11:11AM +0000, LNU, Swati wrote:
> Hello all,
> Is it possible to modify the function
> q^(a) * (eta (Mod(1, m) * q + O(q^(n + 1))))^(24 * a),
> which computes the series expansion of various powers of Ramanujan Delta function and reduces coefficients modulo m, to compute the expansion of various powers of
> the following eta product and reduce coefficients mod m:
> (\eta(z) \eta(3z) \eta(5z) \eta(15 z))^(a).
> I tried changing q -> q^(ka) and flag to a non-zero value for the individual products, but it does not seem to work. Here, k \in {1, 3, 5, 15 \} and a is any positive integer.

You need not change the flag.
GP eta is missing a factor q^(1/24z) so you have to multiply by it to compensate.
but
q^(1/24*z) q^(3/24*z) q^(5/24*z) q^(15/24*z)  = q^z
so that just means multiplying by q.

So you can do this:

etak(k)=eta (Mod(1, m) * q^k + O(q^(n + 1)));
q^(a) * (etak(1)*etak(3)*etak(5)*etak(15))^a

Cheers,
Bill