Proves quantitative Halász theorems for multiplicative functions on nonzero ideals of ℤ[i], with sectorial and short-interval versions under angular non-pretentiousness and non-degeneracy conditions on conjugate primes.
Partition regularity in imaginary quadratic rings of integers
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abstract
We obtain partition regularity results for homogeneous quadratic equations whose parametrized solutions admit nice factorizations into linear forms over rings of integers of imaginary quadratic fields. To do so, we develop number-theoretic results of independent interest on such fields, such as a characterization for aperiodic completely multiplicative functions, the Tur\'an-Kubilius inequality, and a new concentration estimate for multiplicative functions.
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2026 1verdicts
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Hal\'asz theorems for Gaussian ideals in sectors and short intervals
Proves quantitative Halász theorems for multiplicative functions on nonzero ideals of ℤ[i], with sectorial and short-interval versions under angular non-pretentiousness and non-degeneracy conditions on conjugate primes.