Zobrazeno 1 - 10
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pro vyhledávání: '"Mercuri, Pietro"'
Autor:
Dolce, Paolo, Mercuri, Pietro
Let $N>1$ be an integer coprime to $6$ such that $N\notin\{5,7,13\}$ and let $g=g(N)$ be the genus of the modular curve $X_0(N)$. We compute the intersection matrices relative to special fibres of the minimal regular model of $X_0(N)$. Moreover we pr
Externí odkaz:
http://arxiv.org/abs/2304.12068
Autor:
Cherubini, Giacomo, Mercuri, Pietro
We give a complete characterization of the parity of $b_8(n)$, the number of $8$-regular partitions of $n$. Namely, we prove that $b_8(n)$ is odd or even depending on whether or not we have the factorisation $24n+7=p^{4a+1}m^2$, for some prime $p\nmi
Externí odkaz:
http://arxiv.org/abs/2212.11356
Autor:
Mercuri, Pietro
We show that, in many cases, there are infinitely many sets of partitions corresponding to a single analytical Rogers-Ramanujan type identity. This means that a single analytical Rogers-Ramanujan type identity implies the existence of bijections amon
Externí odkaz:
http://arxiv.org/abs/2101.01451
Publikováno v:
Des. Codes Cryptogr. 90, 1347-1368 (2022)
We provide a recipe to construct towers of fields producing high order elements in $\mathrm{GF}(q,2^n)$, for odd $q$, and in $\mathrm{GF}(2,2 \cdot 3^n)$, for $n \ge 1$. These towers are obtained recursively by $x_{n}^2 + x_{n} = v(x_{n - 1})$, for o
Externí odkaz:
http://arxiv.org/abs/2009.10572
Publikováno v:
Alg. Number Th. 16 (2022) 1423-1461
We study the automorphisms of modular curves associated to Cartan subgroups of $\mathrm{GL}_2(\mathbb Z/n\mathbb Z)$ and certain subgroups of their normalizers. We prove that if $n$ is large enough, all the automorphisms are induced by the ramified c
Externí odkaz:
http://arxiv.org/abs/2005.09009
In a work of 1995, Alladi, Andrews, and Gordon provided a generalization of the two Capparelli identities involving certain classes of integer partitions. Inspired by that contribution, in particular as regards the general setting and the tools the a
Externí odkaz:
http://arxiv.org/abs/2004.02666
Publikováno v:
In Journal of Algebra 1 December 2023 635:790-821
Akademický článek
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Autor:
Mercuri, Pietro, Schoof, Rene
In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit equations over $\b
Externí odkaz:
http://arxiv.org/abs/1805.06873
Publikováno v:
J. Number Theory. 195 (2019) 96-114
We present a strategy to obtain explicit equations for the modular double covers associated respectively to both a split and a non-split Cartan subgroup of $\text{GL}_2(\mathbb F_{p})$ with $p$ prime. Then we apply it successfully to the level $13$ c
Externí odkaz:
http://arxiv.org/abs/1706.03988