Re: Question about the use of mfslashexpansion

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

Hello,

The output says that q-series is -8 * q^2 + 64 * q^4 - 96 * q^6 + .... (Order of vanishing at infinity = 2) whereas it should be -8 * q + 64 * q^2 - 96 * q^3 + ....(Order of vanishing at infinity = 1) for eta(z)^8 * eta(2z)^8 | U_2. Also, why does the answer differ when I do the following:

a = mffrometaquo([1, 8; 2, 8]);
b = mfinit(a);
c = 8 * (mfslashexpansion(b, a, [1, 0; 0, 2], 50, 1, &P) +  mfslashexpansion(b, a, [1, 1; 0, 2], 50, 1, &P))

Output: 

[0, 16, -128, 192, 1024, -3360, -1536, 16256, -8192, -32688, 26880, 17472, 12288, 22112, -130048, -40320, 65536, 235296, 261504, -639040, -215040, 195072, -139776, 1099392, -98304, -544400, -176896, -812160, 1040384, -1641120, 322560, 3640832, -524288, 209664, -1882368, -3413760, -2092032, 2568416, 5112320, 265344, 1720320, 173472, -1560576, -10091968, 1118208, 6864480, -8795136, 7562496, 786432, 3339408, 4355200]

I am just confused why doesn't  every output give the following : [0, -8, 64, -96, ....]. I would really apppreciate the clarification. 

Regards,

Swati

"An equation for me has no meaning unless it expresses a thought of God"— Srinivasa Ramanujan.

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From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
Sent: Monday, August 4, 2025 3:16 PM
To: pari-users@pari.math.u-bordeaux.fr <pari-users@pari.math.u-bordeaux.fr>
Subject: Re: Question about the use of mfslashexpansion

 

On Mon, Aug 04, 2025 at 04:54:21PM +0000, LNU, Swati wrote:
> Hello,
> I was trying to understand the use of mfslashexpansion via the following example but it is giving me incorrect answers:
> I am trying to compute the action of eta(z)^8 * eta(2z)^8 acted by U_2 which equals -8 * q + 64 * q^2 - 96 * q^3 + .... On the other hand,
> a = mffrometaquo([1, 8; 2, 8]);
> b = mfinit(a);
> c = 8 * (mfslashexpansion(b, a, [1, 0; 0, 2], 50, 0) +  mfslashexpansion(b, a, [1, 1; 0, 2], 50, 0))
>
> [0, 0, -8, 0, 64, 0, -96, 0, -512, 0, 1680, 0, 768, 0, -8128, 0, 4096, 0, 16344, 0, -13440, 0, -8736, 0, -6144, 0, -11056, 0, 65024, 0, 20160, 0, -32768, 0, -117648, 0, -130752, 0, 319520, 0, 107520, 0, -97536, 0, 69888, 0, -549696, 0, 49152, 0, 272200]

Why do you think the answer is incorect ?

Cheers,
Bill.