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Journal De Theorie Des Nombres De Bordeaux最新文献

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Digital nets in dimension two with the optimal order of L_p discrepancy 具有L_p差异最优阶的二维数字网络
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-04-13 DOI: 10.5802/jtnb.1074
Ralph Kritzinger, F. Pillichshammer
{"title":"Digital nets in dimension two with the optimal order of L_p discrepancy","authors":"Ralph Kritzinger, F. Pillichshammer","doi":"10.5802/jtnb.1074","DOIUrl":"https://doi.org/10.5802/jtnb.1074","url":null,"abstract":"We study the $L_p$ discrepancy of two-dimensional digital nets for finite $p$. In the year 2001 Larcher and Pillichshammer identified a class of digital nets for which the symmetrized version in the sense of Davenport has $L_2$ discrepancy of the order $sqrt{log N}/N$, which is best possible due to the celebrated result of Roth. However, it remained open whether this discrepancy bound also holds for the original digital nets without any modification. \u0000In the present paper we identify nets from the above mentioned class for which the symmetrization is not necessary in order to achieve the optimal order of $L_p$ discrepancy for all $p in [1,infty)$. \u0000Our findings are in the spirit of a paper by Bilyk from 2013, who considered the $L_2$ discrepancy of lattices consisting of the elements $(k/N,{k alpha})$ for $k=0,1,ldots,N-1$, and who gave Diophantine properties of $alpha$ which guarantee the optimal order of $L_2$ discrepancy.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42172651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
The endomorphism ring of projectives and the Bernstein centre 投影子的自同态环与Bernstein中心
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-03-05 DOI: 10.5802/jtnb.1111
A. Pyvovarov
{"title":"The endomorphism ring of projectives and the Bernstein centre","authors":"A. Pyvovarov","doi":"10.5802/jtnb.1111","DOIUrl":"https://doi.org/10.5802/jtnb.1111","url":null,"abstract":"Let $F$ be a local non-archimedean field and $mathcal{O}_F$ its ring of integers. Let $Omega$ be a Bernstein component of the category of smooth representations of $GL_n(F)$, let $(J, lambda)$ be a Bushnell-Kutzko $Omega$-type, and let $mathfrak{Z}_{Omega}$ be the centre of the Bernstein component $Omega$. This paper contains two major results. Let $sigma$ be a direct summand of $mathrm{Ind}_J^{GL_n(mathcal{O}_F)} lambda$. We will begin by computing $mathrm{ctext{--} Ind}_{GL_n(mathcal{O}_F)}^{GL_n(F)} sigmaotimes_{mathfrak{Z}_{Omega}}kappa(mathfrak{m})$, where $kappa(mathfrak{m})$ is the residue field at maximal ideal $mathfrak{m}$ of $mathfrak{Z}_{Omega}$, and the maximal ideal $mathfrak{m}$ belongs to a Zariski-dense set in $mathrm{Spec}: mathfrak{Z}_{Omega}$. This result allows us to deduce that the endomorphism ring $mathrm{End}_{GL_n(F)}(mathrm{ctext{--} Ind}_{GL_n(mathcal{O}_F)}^{GL_n(F)} sigma)$ is isomorphic to $mathfrak{Z}_{Omega}$, when $sigma$ appears with multiplicity one in $mathrm{Ind}_J^{GL_n(mathcal{O}_F)} lambda$.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44579529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Reduction of certain crystalline representations and local constancy in the weight space 某些晶体表示的约简和权重空间中的局部恒定性
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-23 DOI: 10.5802/jtnb.1110
S. Bhattacharya
{"title":"Reduction of certain crystalline representations and local constancy in the weight space","authors":"S. Bhattacharya","doi":"10.5802/jtnb.1110","DOIUrl":"https://doi.org/10.5802/jtnb.1110","url":null,"abstract":"We study the mod $p$ reduction of crystalline local Galois representations of dimension 2 under certain conditions on its weight and slope. Berger showed that for a fixed non-zero trace of the Frobenius, the reduction process is locally constant for varying weights. By explicit computation we obtain an upper bound that is a linear function of the slope, for the radius of this local constancy around some special points in the weight space.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49127188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
Root number of twists of an elliptic curve 椭圆曲线的扭曲根数
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-16 DOI: 10.5802/jtnb.1112
Julie Desjardins
{"title":"Root number of twists of an elliptic curve","authors":"Julie Desjardins","doi":"10.5802/jtnb.1112","DOIUrl":"https://doi.org/10.5802/jtnb.1112","url":null,"abstract":"We give an explicit description of the behaviour of the root number in the family given by the twists of an elliptic curve $E$ by the rational values of a polynomial $f(T)$. In particular, we give a criterion (on $f$ depending on $E$) for the family to have a constant root number over $mathbb{Q}$. This completes a work of Rohrlich: we detail the behaviour of the root number when $E$ has bad reduction over $mathbb{Q}^{ab}$ and we treat the cases $j(E)=0,1728$ which were not considered by Rohrlich.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46891197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 8
Répartition galoisienne ultramétrique d’une classe d’isogénie de courbes elliptiques : Le cas de la mauvaise réduction. Application aux hauteurs locales. 椭圆曲线等距类的超度量伽罗瓦分布:差约简的情况。适用于局部高度。
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-01 DOI: 10.5802/jtnb.1013
Rodolphe Richard
{"title":"Répartition galoisienne ultramétrique d’une classe d’isogénie de courbes elliptiques : Le cas de la mauvaise réduction. Application aux hauteurs locales.","authors":"Rodolphe Richard","doi":"10.5802/jtnb.1013","DOIUrl":"https://doi.org/10.5802/jtnb.1013","url":null,"abstract":"","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"13 1","pages":"1-18"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74036534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
A note on the regularity of the Diophantine pair $protect lbrace k,4kpm 4protect rbrace $ 丢番图对$protect rbrace k,4kpm 4protect rbrace $的正则性注释
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-01 DOI: 10.5802/JTNB.1055
B. He, Keli Pu, R. Shen, A. Togbé
{"title":"A note on the regularity of the Diophantine pair $protect lbrace k,4kpm 4protect rbrace $","authors":"B. He, Keli Pu, R. Shen, A. Togbé","doi":"10.5802/JTNB.1055","DOIUrl":"https://doi.org/10.5802/JTNB.1055","url":null,"abstract":"","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"203 1","pages":"879-892"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76025569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
Counting points on the Fricke-Macbeath curve over finite fields 有限域上的Fricke-Macbeath曲线上的点计数
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-01 DOI: 10.5802/JTNB.1019
Jaap Top, Carlo Verschoor
{"title":"Counting points on the Fricke-Macbeath curve over finite fields","authors":"Jaap Top, Carlo Verschoor","doi":"10.5802/JTNB.1019","DOIUrl":"https://doi.org/10.5802/JTNB.1019","url":null,"abstract":"The Fricke-Macbeath curve is a smooth projective algebraic curve of genus 7 with automorphism group PSL₂(픽₈). We recall two models of it (introduced, respectively, by Maxim Hendriks and by Bradley Brock) defined over ℚ, and we establish an explicit isomorphism defined over ℚ( −7 ) between these models. Moreover, we decompose up to isogeny over ℚ the jacobian of one of these models. As a consequence we obtain a simple formula for the number of points over 픽q on (the reduction of) this model, in terms of the elliptic curve with equation y² = x³ + x² − 114x − 127. Moreover, twists by elements of PSL₂(픽₈) of the curve over finite fields are described. The curve leads to a number of new records as maintained on manYPoints of curves of genus 7 with many rational points over finite fields.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"8 1","pages":"117-129"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75724774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Cubic polynomials defining monogenic fields with the same discriminant 用相同的判别式定义单基因域的三次多项式
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-01 DOI: 10.5802/JTNB.1061
C. Davis, B. K. Spearman, Jeewon Yoo
{"title":"Cubic polynomials defining monogenic fields with the same discriminant","authors":"C. Davis, B. K. Spearman, Jeewon Yoo","doi":"10.5802/JTNB.1061","DOIUrl":"https://doi.org/10.5802/JTNB.1061","url":null,"abstract":"Let K be a number field with ring of integers OK . K is said to be monogenic if OK = Z[θ] for some θ ∈ OK . Monogeneity of a number field is not always guaranteed. Furthermore, it is rare for two number fields to have the same discriminant, thus finding fields with these two properties is an interesting problem. In this paper we show that there exist infinitely many triples of polynomials defining distinct monogenic cubic fields with the same discriminant.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"53 1","pages":"991-996"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89208498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
An exponential sum estimate for systems with linear polynomials 线性多项式系统的指数和估计
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-01 DOI: 10.5802/JTNB.1035
S. Yamagishi
{"title":"An exponential sum estimate for systems with linear polynomials","authors":"S. Yamagishi","doi":"10.5802/JTNB.1035","DOIUrl":"https://doi.org/10.5802/JTNB.1035","url":null,"abstract":"","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"18 1","pages":"485-499"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75884221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Heights and representations of split tori 分割环面的高度和表示
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2018-01-01 DOI: 10.5802/jtnb.1015
V. Talamanca
{"title":"Heights and representations of split tori","authors":"V. Talamanca","doi":"10.5802/jtnb.1015","DOIUrl":"https://doi.org/10.5802/jtnb.1015","url":null,"abstract":"Let Gm denote the d-dimensional split torus defined over a number field k. To each Gm-module E we associate a height function hE defined by means of the spectral height on GL(E). This gives rise to a height pairing between the monoid of irreducible Gm-modules of Gm and the group Gm ( k ) . Our main results are a characterization of those Gm-modules E for which hE satisfeis Northcott’s finiteness theorem, the determination of the kernels of the height pairing, as well as, for a few special classes of Gm-modules, of the group of automorphisms that preserve hE .","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"SE-13 1","pages":"41-57"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84641472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
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