6 citations · 13 across the 10 of their papers we have counts for
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Multigraded Koszul complexes, filter-regular sequences and lower bounds for the multiplicity of the resultant
Luca Ghidelli
The Rémond resultant attached to a multiprojective variety and a sequence of multihomogeneous polynomials is a polynomial form in the coefficients of the polynomials, which vanishe…
On gaps between sums of four fourth powers
Luca Ghidelli
We prove that for almost all there is a sum of four fourth powers in the interval , for all .
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…
Arbitrarily long gaps between the values of positive-definite cubic and biquadratic diagonal forms
Luca Ghidelli
For , we prove the existence of arbitrarily long sequences of consecutive integers none of which is a sum of nonnegative -th powers. More generally, we study the exis…
On rich and poor directions determined by a subset of a finite plane
Luca Ghidelli
We generalize to sets with cardinality more than a theorem of Rédei and Szőnyi on the number of directions determined by a subset of the finite plane . A …