Mathematical Research Letters最新文献_第7页

Local and global densities for Weierstrass models of elliptic curves 椭圆曲线Weierstrass模型的局部和全局密度

3区数学

Mathematical Research Letters Pub Date : 2023-01-01 DOI: 10.4310/mrl.2023.v30.n2.a5

J. E. Cremona, M. Sadek

{"title":"Local and global densities for Weierstrass models of elliptic curves","authors":"J. E. Cremona, M. Sadek","doi":"10.4310/mrl.2023.v30.n2.a5","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n2.a5","url":null,"abstract":"We prove local results on the $p$-adic density of elliptic curves over $mathbb{Q}_p$ with different reduction types, together with global results on densities of elliptic curves over $mathbb{Q}$ with specified reduction types at one or more (including infinitely many) primes. These global results include: the density of integral Weierstrass equations which are minimal models of semistable elliptic curves over $mathbb{Q}$ (that is, elliptic curves with square-free conductor) is $1/zeta(2)approx60.79%$, the same as the density of square-free integers; the density of semistable elliptic curves over $mathbb{Q}$ is $zeta(10)/zeta(2)approx60.85%$; the density of integral Weierstrass equations which have square-free discriminant is $prod_pleft(1-frac{2}{p^2}+frac{1}{p^3}right) approx 42.89%$, which is the same (except for a different factor at the prime $2$) as the density of monic integral cubic polynomials with square-free discriminant (and agrees with a previous result of Baier and Browning for short Weierstrass equations); and the density of elliptic curves over $mathbb{Q}$ with square-free minimal discriminant is $zeta(10)prod_pleft(1-frac{2}{p^2}+frac{1}{p^3}right)approx42.93%$. The local results derive from a detailed analysis of Tate's Algorithm, while the global ones are obtained through the use of the Ekedahl Sieve, as developed by Poonen, Stoll, and Bhargava.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135799035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 25

Derived categories of Quot schemes of locally free quotients via categorified Hall products 利用已分类的霍尔积导出了局部自由商的“方案”的类别

IF 1 3区数学

Mathematical Research Letters Pub Date : 2023-01-01 DOI: 10.4310/mrl.2023.v30.n1.a10

Yukinobu Toda

引用次数: 0

Refinements of strong multiplicity one for $mathrm{GL}(2)$ $mathrm｛GL｝（2）的强重数一的精化$

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-03-20 DOI: 10.4310/mrl.2022.v29.n2.a11

PENG-JIE Wong

引用次数: 0

The Surface Group Conjectures for groups with two generators 具有两个发生器的群的表面群猜想

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-02-22 DOI: 10.4310/mrl.2023.v30.n1.a5

Giles Gardam, Dawid Kielak, Alan D. Logan

引用次数: 2

Internal stabilization for KdV-BBM equation on a periodic domain 周期域上KdV-BBM方程的内镇定

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n6.a4

Melek Jellouli, M. Khenissi

引用次数: 0

The local information of difference equations 差分方程的局部信息

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n1.a5

Moisés Herradón Cueto

引用次数: 0

Diagrams of $star$-trisections $星$-三切分图

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n6.a1

Rom'an Aranda, Jesse Moeller

引用次数: 0

Convex hull property for ancient harmonic map heat flows 古调和图热流的凸壳性

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n5.a12

C. Sung

引用次数: 0

New $k$-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem 孤立超曲面奇点的新$k$-th Yau代数及弱torelli型定理

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n2.a7

Naveed Hussain, S. Yau, Huaiqing Zuo

{"title":"New $k$-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem","authors":"Naveed Hussain, S. Yau, Huaiqing Zuo","doi":"10.4310/mrl.2022.v29.n2.a7","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n2.a7","url":null,"abstract":"Let V be a hypersurface with an isolated singularity at the origin deﬁned by the holomorphic function f : ( C n , 0) → ( C , 0). The Yau algebra L ( V ) is deﬁned to be the Lie algebra of derivations of the moduli algebra A ( V ) := O n / ( f, ∂f∂x 1 , · · · , ∂f∂x n ), i.e., L ( V ) = Der( A ( V ) , A ( V )). It is known that L ( V ) is a ﬁnite dimensional Lie algebra and its dimension λ ( V ) is called Yau number. In this paper, we introduce a new series of Lie algebras, i.e., k -th Yau algebras L k ( V ), k ≥ 0, which are a generalization of Yau algebra. L k ( V ) is deﬁned to be the Lie algebra of derivations of the k th moduli algebra A k ( V ) := O n / ( f, m k J ( f )) , k ≥ 0, i.e., L k ( V ) = Der( A k ( V ) , A k ( V )), where m is the maximal ideal of O n . The k -th Yau number is the dimension of L k ( V ) which we denote as λ k ( V ). In particular, L 0 ( V ) is exactly the Yau algebra, i.e., L 0 ( V ) = L ( V ) , λ 0 ( V ) = λ ( V ). These numbers λ k ( V ) are new numerical analytic invariants of singularities. In this paper we obtain the weak Torelli-type theorems of simple elliptic singularities using Lie algebras L 1 ( V ) and L 2 ( V ). We shall also characterize the simple singularities completely using L 1 ( V ).","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Symplectic duality for $T^ast Gr(k, n)$ T^ast Gr(k, n)的辛对偶性

IF 1 3区数学

Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n3.a3

Hunter Dinkins

引用次数: 0