Demonstrates convergence of lattice sums in SL+(2, ℤ), suggesting a new proof method for mathematical identities.
We study lattice sums [Formula: see text] taken over [Formula: see text], i.e. the set of pairs [Formula: see text] of primitive lattice vectors in [Formula: see text] with [Formula: see text]. We prove convergence of these and similar (determinant weighted) sums and introduce a new telescoping method on [Formula: see text] that yields, in particular, [Formula: see text] and a short proof of Zagier’s identity [Formula: see text].
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Nikita Kalinin (2026) studied this question.
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