Re: [sage-devel] Gauss sum for the Dirichet character modulo 1

[Nicolás Sirolli]

Sure! I'll do it.

El jueves, 5 de abril de 2018, 12:15:30 (UTC-3), David Loeffler escribió:
>
> Sounds reasonable to me. Can you open a trac ticket for this?
>
> On 28 March 2018 at 18:01, Nicolás Sirolli  > wrote:
>
>> The Gauss sum for the Dirichlet character modulo 1 is equal to 1, but:
>>
>> sage: G = DirichletGroup(1)
>> sage: chi = G.list()[0]
>> sage: chi.gauss_sum()
>> 0
>>
>> The output is zero because the gauss_sum function in 
>> modular/dirichlet.py, after some preliminaries, computes the following:
>>
>> for c in chi.values()[1:]:
>> z *= zeta
>> g += L(c)*z
>> return g
>>
>>
>> If chi.modulus() > 1, then chi.values()[0] equals 0, so it can be skipped 
>> in the sum above. But in this case, it equals 1 and needs to be included in 
>> the sum
>>
>> I'm using 8.2 beta 7.
>>
>> Best,
>> Nicolás.
>>
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>
>

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Re: [sage-devel] Gauss sum for the Dirichet character modulo 1

[David Loeffler]

Sounds reasonable to me. Can you open a trac ticket for this?

On 28 March 2018 at 18:01, Nicolás Sirolli  wrote:

> The Gauss sum for the Dirichlet character modulo 1 is equal to 1, but:
>
> sage: G = DirichletGroup(1)
> sage: chi = G.list()[0]
> sage: chi.gauss_sum()
> 0
>
> The output is zero because the gauss_sum function in modular/dirichlet.py,
> after some preliminaries, computes the following:
>
> for c in chi.values()[1:]:
> z *= zeta
> g += L(c)*z
> return g
>
>
> If chi.modulus() > 1, then chi.values()[0] equals 0, so it can be skipped
> in the sum above. But in this case, it equals 1 and needs to be included in
> the sum
>
> I'm using 8.2 beta 7.
>
> Best,
> Nicolás.
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-devel" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-devel+unsubscr...@googlegroups.com.
> To post to this group, send email to sage-devel@googlegroups.com.
> Visit this group at https://groups.google.com/group/sage-devel.
> For more options, visit https://groups.google.com/d/optout.
>

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