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SUMS OF DISTINCT INTEGRAL SQUARES IN
, 
AND 
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 85 / Issue 1 / February 2012
- Published online by Cambridge University Press:
- 08 September 2011, pp. 1-10
- Print publication:
- February 2012
-
- Article
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- You have access
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In this article, we determine all the totally positive integers of
which can be represented as sums of distinct integral squares, where m=2, 3, 6.
, 
AND 
which can be represented as sums of distinct integral squares, where Hecke
$L$-Functions and the Distribution of Totally Positive Integers
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- Journal:
- Canadian Journal of Mathematics / Volume 59 / Issue 4 / 01 August 2007
- Published online by Cambridge University Press:
- 20 November 2018, pp. 673-695
- Print publication:
- 01 August 2007
-
- Article
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- You have access
- Export citation
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Let
$K$ be a totally real number field of degree 
$n$. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained from geometric considerations. This result depends on unfolding an integral over a compact torus.
