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Communications in Number Theory and Physics最新文献

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Equivariant derived equivalence and rational points on K3 surfaces K3曲面上等变导数等价与有理点
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-05-28 DOI: 10.4310/cntp.2023.v17.n2.a2
B. Hassett, Y. Tschinkel
{"title":"Equivariant derived equivalence and rational points on K3 surfaces","authors":"B. Hassett, Y. Tschinkel","doi":"10.4310/cntp.2023.v17.n2.a2","DOIUrl":"https://doi.org/10.4310/cntp.2023.v17.n2.a2","url":null,"abstract":"We study arithmetic properties of derived equivalent K3 surfaces over the field of Laurent power series, using the equivariant geometry of K3 surfaces with cyclic groups actions.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43033009","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: 1
Diophantine equations with sum of cubes and cube of sum 丢番图方程的和立方和立方的和
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-04-27 DOI: 10.4310/cntp.2022.v16.n2.a4
Bogdan A. Dobrescu, Patrick J. Fox
{"title":"Diophantine equations with sum of cubes and cube of sum","authors":"Bogdan A. Dobrescu, Patrick J. Fox","doi":"10.4310/cntp.2022.v16.n2.a4","DOIUrl":"https://doi.org/10.4310/cntp.2022.v16.n2.a4","url":null,"abstract":"We solve Diophantine equations of the type $a(x^3+y^3+z^3)=(x+y+z)^3$, where $x$, $y$, $z$ are integer variables, and the coefficient $a neq 0$ is rational. We show that there are infinite families of such equations, including those where $a$ is any cube or certain rational fractions, that have nontrivial solutions. There are also infinite families of equations that do not have any nontrivial solution, including those where $1/a=1-24/m$ with restrictions on the integer $m$. The equations can be represented by elliptic curves unless $a=9$ or $1$, and any elliptic curve of nonzero $j$-invariant and torsion group $mathbb{Z}/3kmathbb{Z}$ for $k=2,3,4$, or $mathbb{Z}/2mathbb{Z} times mathbb{Z}/6mathbb{Z}$ corresponds to a particular $a$. We prove that for any $a$ the number of nontrivial solutions is at most $3$ or is infinite, and for integer $a$ it is either $0$ or $infty$. For $a=9$, we find the general solution, which depends on two integer parameters. These cubic equations are important in particle physics, because they determine the fermion charges under the $U(1)$ gauge group.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"30 3","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520810","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: 0
Modular parametrization as Polyakov path integral: cases with CM elliptic curves as target spaces 作为Polyakov路径积分的模参数化:以CM椭圆曲线为目标空间的情况
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-04-27 DOI: 10.4310/cntp.2022.v16.n2.a3
Satoshi Kondo, Taizan Watari
{"title":"Modular parametrization as Polyakov path integral: cases with CM elliptic curves as target spaces","authors":"Satoshi Kondo, Taizan Watari","doi":"10.4310/cntp.2022.v16.n2.a3","DOIUrl":"https://doi.org/10.4310/cntp.2022.v16.n2.a3","url":null,"abstract":"For an elliptic curve $E$ over an abelian extension $k/K$ with CM by $K$ of Shimura type, the L-functions of its $[k:K]$ Galois representations are Mellin transforms of Hecke theta functions; a modular parametrization (surjective map) from a modular curve to $E$ pulls back the $1$-forms on $E$ to give the Hecke theta functions. This article refines the study of our earlier work and shows that certain class of chiral correlation functions in Type II string theory with $[E]_mathbb{C}$ ($E$ as real analytic manifold) as a target space yield the same Hecke theta functions as objects on the modular curve. The Kähler parameter of the target space $[E]_mathbb{C}$ in string theory plays the role of the index (partially ordered) set in defining the projective/direct limit of modular curves.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"39 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520818","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: 0
Mirror symmetry of Calabi-Yau manifolds fibered by $(1,8)$-polarized abelian surfaces 由$(1,8)$-极化阿贝尔曲面纤维的Calabi-Yau流形的镜像对称性
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-04-27 DOI: 10.4310/cntp.2022.v16.n2.a1
Shinobu Hosono, Hiromichi Takagi
{"title":"Mirror symmetry of Calabi-Yau manifolds fibered by $(1,8)$-polarized abelian surfaces","authors":"Shinobu Hosono, Hiromichi Takagi","doi":"10.4310/cntp.2022.v16.n2.a1","DOIUrl":"https://doi.org/10.4310/cntp.2022.v16.n2.a1","url":null,"abstract":"We study mirror symmetry of a family of Calabi–Yau manifolds fibered by $(1,8)$-polarized abelian surfaces with Euler characteristic zero. By describing the parameter space globally, we find all expected boundary points (LCSLs), including those correspond to Fourier–Mukai partners. Applying mirror symmetry at each boundary point, we calculate Gromov–Witten invariants $(g leq 2)$ and observe nice (quasi-)modular properties in their potential functions. We also describe degenerations of Calabi–Yau manifolds over each boundary point.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"38 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520820","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: 0
Resurgent Stokes data for Painlevé equations and two-dimensional quantum (super) gravity painlev<s:1>方程和二维量子(超)引力的复兴Stokes数据
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-03-25 DOI: 10.4310/cntp.2023.v17.n2.a5
Salvatore Baldino, R. Schiappa, M. Schwick, Roberto Vega
{"title":"Resurgent Stokes data for Painlevé equations and two-dimensional quantum (super) gravity","authors":"Salvatore Baldino, R. Schiappa, M. Schwick, Roberto Vega","doi":"10.4310/cntp.2023.v17.n2.a5","DOIUrl":"https://doi.org/10.4310/cntp.2023.v17.n2.a5","url":null,"abstract":"Resurgent-transseries solutions to Painleve equations may be recursively constructed out of these nonlinear differential-equations -- but require Stokes data to be globally defined over the complex plane. Stokes data explicitly construct connection-formulae which describe the nonlinear Stokes phenomena associated to these solutions, via implementation of Stokes transitions acting on the transseries. Nonlinear resurgent Stokes data lack, however, a first-principle computational approach, hence are hard to determine generically. In the Painleve I and Painleve II contexts, nonlinear Stokes data get further hindered as these equations are resonant, with non-trivial consequences for the interconnections between transseries sectors, bridge equations, and associated Stokes coefficients. In parallel to this, the Painleve I and Painleve II equations are string-equations for two-dimensional quantum (super) gravity and minimal string theories, where Stokes data have natural ZZ-brane interpretations. This work computes for the first time the complete, analytical, resurgent Stokes data for the first two Painleve equations, alongside their quantum gravity or minimal string incarnations. The method developed herein, dubbed\"closed-form asymptotics\", makes sole use of resurgent large-order asymptotics of transseries solutions -- alongside a careful analysis of the role resonance plays. Given its generality, it may be applicable to other distinct (nonlinear, resonant) problems. Results for analytical Stokes coefficients have natural structures, which are described, and extensive high-precision numerical tests corroborate all analytical predictions. Connection-formulae are explicitly constructed, with rather simple and compact final results encoding the full Stokes data, and further allowing for exact monodromy checks -- hence for an analytical proof of our results.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42713480","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: 2
Fourier expansions of vector-valued automorphic functions with non-unitary twists 具有非幺正扭转的向量值自同构函数的傅里叶展开式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-01-12 DOI: 10.4310/CNTP.2023.v17.n1.a5
Ksenia Fedosova, A. Pohl, J. Rowlett
{"title":"Fourier expansions of vector-valued automorphic functions with non-unitary twists","authors":"Ksenia Fedosova, A. Pohl, J. Rowlett","doi":"10.4310/CNTP.2023.v17.n1.a5","DOIUrl":"https://doi.org/10.4310/CNTP.2023.v17.n1.a5","url":null,"abstract":"We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on invertibility or unitarity are made. Examples of such eigenfunctions include vector-valued twisted automorphic forms of Fuchsian groups. We further provide a detailed description of the Fourier coefficients and explicitly identify each of their constituents, which intimately depend on the eigenvalues of the twisting endomorphism and the size of its Jordan blocks. In addition, we determine the growth properties of the Fourier coefficients.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70423059","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: 1
On quasi-tame Looijenga pairs 关于拟驯服的Looijenga对
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-01-05 DOI: 10.4310/cntp.2023.v17.n2.a3
A. Brini, Yannik Schuler
{"title":"On quasi-tame Looijenga pairs","authors":"A. Brini, Yannik Schuler","doi":"10.4310/cntp.2023.v17.n2.a3","DOIUrl":"https://doi.org/10.4310/cntp.2023.v17.n2.a3","url":null,"abstract":"We prove a conjecture of Bousseau, van Garrel and the first-named author relating, under suitable positivity conditions, the higher genus maximal contact log Gromov-Witten invariants of Looijenga pairs to other curve counting invariants of Gromov-Witten/Gopakumar-Vafa type. The proof consists of a closed-form $q$-hypergeometric resummation of the quantum tropical vertex calculation of the log invariants in presence of infinite scattering. The resulting identity of $q$-series appears to be new and of independent combinatorial interest.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46316385","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: 2
$T overline{T}$-deformed modular forms $Toverline{T}$-变形模块形式
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-01-03 DOI: 10.4310/CNTP.2022.v16.n3.a1
J. Cardy
{"title":"$T overline{T}$-deformed modular forms","authors":"J. Cardy","doi":"10.4310/CNTP.2022.v16.n3.a1","DOIUrl":"https://doi.org/10.4310/CNTP.2022.v16.n3.a1","url":null,"abstract":": Certain objects of conformal field theory, for example partition functions on the rectangle and the torus, and one-point functions on the torus, are either invariant or transform simply under the modular group, properties which should be preserved under the T T deformation. The formulation and proof of this statement in fact extents to more general functions such as T T deformed modular and Jacobi forms. We show that the deformation acts simply on their Mellin transform, multiplying it by a universal entire function. Finally we show that Maass forms on the torus are eigenfunctions of the T T deformation.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44335694","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: 0
On a class of non-simply connected Calabi-Yau $3$-folds with positive Euler characteristic 一类具有正欧拉特征的非单连通Calabi-Yau $3$-折叠
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2022-01-01 DOI: 10.4310/cntp.2022.v16.n1.a-karayayla
Tolga Karayayla
{"title":"On a class of non-simply connected Calabi-Yau $3$-folds with positive Euler characteristic","authors":"Tolga Karayayla","doi":"10.4310/cntp.2022.v16.n1.a-karayayla","DOIUrl":"https://doi.org/10.4310/cntp.2022.v16.n1.a-karayayla","url":null,"abstract":"","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70423048","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: 1
On the mixed-twist construction and monodromy of associated Picard–Fuchs systems 关于相关Picard-Fuchs系统的混合扭曲结构和单调性
IF 1.9 3区 数学
Communications in Number Theory and Physics Pub Date : 2021-08-16 DOI: 10.4310/CNTP.2022.v16.n3.a2
Andreas Malmendier, Michael T. Schultz
{"title":"On the mixed-twist construction and monodromy of associated Picard–Fuchs systems","authors":"Andreas Malmendier, Michael T. Schultz","doi":"10.4310/CNTP.2022.v16.n3.a2","DOIUrl":"https://doi.org/10.4310/CNTP.2022.v16.n3.a2","url":null,"abstract":". We use the mixed-twist construction of Doran and Malmendier to obtain a multi-parameter family of K3 surfaces of Picard rank ρ ≥ 16. Upon identifying a particular Jacobian elliptic fibration on its general member, we determine the lattice polarization and the Picard-Fuchs system for the family. We construct a sequence of restrictions that lead to extensions of the polarization by two-elementary lattices. We show that the Picard-Fuchs operators for the restricted families coincide with known resonant hypergeometric systems. Second, for the one-parameter mirror families of deformed Fermat hypersurfaces we show that the mixed-twist construction produces a non-resonant GKZ system for which a basis of solutions in the form of absolutely convergent Mellin-Barnes integrals exists whose monodromy we compute explicitly.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44667130","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: 0
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