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Session 1. Analytic Number Theory |
Sums of squares coprime in pairs |
| Joerg Brüdern, Universität Göttingen, Germany |
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We consider the representation of natural numbers in the proposed
form, with three and four variables. Our work yields an asymptotic
formula for the number of such representations. The method is
effective for sums of four squares, answering affirmatively a
question of Schinzel. For sums of three squares, Siegel's lower
bound for Dirichlet \(L\) series near \(1\) is needed, rendering the
result ineffective.
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