[seqfan] Re: Desired: "number of representations on n as the sum of two squares and three biquadrates"

[Charles Greathouse]

It's pretty easy to get the number of ordered representations. The PARI
code:

lim = 10000;
W2=2*sum(i=0,lim^(1/2),x^i^2,O(x^lim))-1;
W4=2*sum(i=0,lim^(1/4),x^i^4,O(x^lim))-1;
Vec(W2^2*W4^3)

gives the first 10,000 terms. I haven't looked to see if the paper uses
ordered or unordered representations.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Thu, Dec 27, 2012 at 9:09 PM, Jonathan Post <jvospost3 at gmail.com> wrote:

> because we have a good paper on the asymptotics:
>
> On Waring's problem: two squares and three biquadrates
> John B. Friedlander, Trevor D. Wooley
> (Submitted on 8 Nov 2012)
>
> We investigate sums of mixed powers involving two squares and three
> biquadrates. In particular, subject to the truth of the Generalised
> Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that
> all large natural numbers n with 8 not dividing n, n not congruent to
> 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2
> squares and 3 biquadrates.
>
> Subjects:       Number Theory (math.NT)
> MSC classes:    11P05, 11N36, 11P55
> Cite as:        arXiv:1211.1823 [math.NT]
>         (or arXiv:1211.1823v1 [math.NT] for this version)
> Submission history
> From: Trevor Wooley [view email]
> [v1] Thu, 8 Nov 2012 10:51:03 GMT (13kb)
>
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