Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Ghidelli, Luca"'
Autor:
Ghidelli, Luca
If the product of two monic polynomials with real nonnegative coefficients has all coefficients equal to 0 or 1, does it follow that all the coefficients of the two factors are also equal to 0 or 1? Here is an equivalent formulation of this intriguin
Externí odkaz:
http://arxiv.org/abs/2209.09843
Autor:
Ghidelli, Luca
One main goal of this thesis is to show that for every K it is possible to find K consecutive natural numbers that cannot be written as sums of three nonnegative cubes. Since it is believed that approximately 10% of all natural numbers can be written
Externí odkaz:
http://hdl.handle.net/10393/40014
Autor:
Ghidelli, Luca, Lacini, Justin
Let X be a smooth complex projective variety of dimension n. We prove bounds on Fujita's basepoint freeness conjecture that grow as nloglog(n).
Comment: 25 pages
Comment: 25 pages
Externí odkaz:
http://arxiv.org/abs/2107.11705
Autor:
Coppola, Giovanni, Ghidelli, Luca
We call $R_G(a):=\sum_{q=1}^{\infty}G(q)c_q(a)$ the 'Ramanujan series', of coefficient $G:$N$\to$C, where $c_q(a)$ is the well-known Ramanujan sum. We study the convergence of this series (a preliminary step, to study Ramanujan expansions and define
Externí odkaz:
http://arxiv.org/abs/2009.14121
Autor:
Coppola, Giovanni, Ghidelli, Luca
The null-function $0(a):=0$, $\forall a\in $N, has Ramanujan expansions: $0(a)=\sum_{q=1}^{\infty}(1/q)c_q(a)$ (where $c_q(a):=$ Ramanujan sum), given by Ramanujan, and $0(a)=\sum_{q=1}^{\infty}(1/\varphi(q))c_q(a)$, given by Hardy ($\varphi:=$ Euler
Externí odkaz:
http://arxiv.org/abs/2005.14666
Autor:
Ghidelli, Luca
The R\'emond resultant attached to a multiprojective variety and a sequence of multihomogeneous polynomials is a polynomial form in the coefficients of the polynomials, which vanishes if and only if the polynomials have a common zero on the variety.
Externí odkaz:
http://arxiv.org/abs/1912.04047
Autor:
Ghidelli, Luca
We prove that for almost all $N$ there is a sum of four fourth powers in the interval $(N-N^\gamma,N]$, for all $\gamma>4059/16384=0.24774..$.
Comment: 22 pages
Comment: 22 pages
Externí odkaz:
http://arxiv.org/abs/1910.05079
Autor:
Ghidelli, Luca
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 result of Bradshaw by showing that such series is not a cubic (resp. biqua
Externí odkaz:
http://arxiv.org/abs/1910.05076
Autor:
Ghidelli, Luca
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 existence of gaps between the values $\leq N$ of diagonal forms of degree
Externí odkaz:
http://arxiv.org/abs/1910.05070
Autor:
Ghidelli, Luca
We generalize to sets with cardinality more than $p$ a theorem of R\'edei and Sz\H{o}nyi on the number of directions determined by a subset $U$ of the finite plane $\mathbb F_p^2$. A $U$-rich line is a line that meets $U$ in at least $\#U/p+1$ points
Externí odkaz:
http://arxiv.org/abs/1903.03881