Luca Ghidelli

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20172026

most citedMultigraded Koszul complexes, filter-regular sequences and lower bounds for the multiplicity of the resultant

1 citations · 3 across the 8 of their papers we have counts for

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Showing 2019 · math.NTShow all

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math.NT2019

On gaps between sums of four fourth powers

Luca Ghidelli

We prove that for almost all $N$ there is a sum of four fourth powers in the interval $(N - N^{γ}, N]$ , for all $γ > 4059/16384 = 0.24774..$ .

math.NT2019★ 1 cited

Arithmetic properties of cubic and biquadratic theta series

Luca Ghidelli

A cubic (resp. biquadratic) theta series is a power series whose n-th coefficient is equal to 1 if n is a perfect cube (resp. fourth power) and zero otherwise. We improve on a resu…

math.NT2019

Arbitrarily long gaps between the values of positive-definite cubic and biquadratic diagonal forms

Luca Ghidelli

For $s = 3, 4$ , we prove the existence of arbitrarily long sequences of consecutive integers none of which is a sum of $s$ nonnegative $s$ -th powers. More generally, we study the exis…