Re: Regard hecke operators in half integer weight setting

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sun, Sep 15, 2024 at 09:43:26AM +0200, Bill Allombert wrote:
> On Sun, Sep 15, 2024 at 02:45:16AM +0000, LNU, Swati wrote:
> > Dear Professor,
> > This command itself gives the error.
> > 
> > S(f, p, k) = {f = truncate(f); sum(n = 1, poldegree(f), (polcoeff(f, (n * p^2))) + (kronecker(-4, n)^(k - (1/2)) * kronecker(12 * n,p) * p^(k - (3/2)) * polcoeff(f, n)) + (sumdiv(n, p, p^((2 * k)- 2) * polcoeff(f, n/p^2))) * q^n) + O(q^(poldegree(f) + 1));}
> 
> Ah OK! But there is no error on my computer:
> 
> parisizemax = 4000002048, primelimit = 500000, nbthreads = 8
> ? S(f, p, k) = {f = truncate(f); sum(n = 1, poldegree(f), (polcoeff(f, (n * p^2))) + (kronecker(-4, n)^(k - (1/2)) * kronecker(12 * n,p)
> * p^(k - (3/2)) * polcoeff(f, n)) + (sumdiv(n, p, p^((2 * k)- 2) * polcoeff(f, n/p^2))) * q^n) + O(q^(poldegree(f) + 1));}
                                                                                 ^^^^^
n/p^2 has no reason to be an integer, so this is not valid.
Maybe you want to restrict the sum to primes such that p^2 divides n ?
then add if(n%p^2==0,....,0) iun the sum.

Cheers,
Bill.