For a vector $\mathbf a=(a_1,\ldots,a_r)$ of positive integers we prove
formulas for the restricted partition function $p_{\mathbf a}(n): = $ the
number of integer solutions $(x_1,\dots,x_r)$ to $\sum_{j=1}^r a_jx_j=n$ with
$x_1\geq 0, \ldots, x_r\geq 0$ and its polynomial part.Comment: 21 pages, to appear in The Ramanujan Journa
We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.
We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
Let {K/\mathbb{Q}} be a finite Galois extension.
Let {\chi_{1},\ldots,\chi_{r}} be {r\geq 1} distinct characters of the Galois group with the associated Artin L-functions {L(s,\chi_{1}),\ldots,L(s,\chi_{r})}.
Let {m\geq 0}.
We prove that the derivatives {L^{(k)}(s,\chi_{j})}, {1\leq j\leq r}, {0\leq k\leq m}, are linearly independent over the field of meromorphic functions of order {<1}.
From this it follows that the L-functions corresponding to the irreducible characters are algebraically independent over the field of meromorphic functions of order {<1}.
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