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Resurgent transseries, mould calculus and Connes-Kreimer Hopf algebra 复兴的横列，模微积分和Connes-Kreimer Hopf代数
4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-11-01 DOI: 10.3792/pjaa.99.013
Shingo Kamimoto
{"title":"Resurgent transseries, mould calculus and Connes-Kreimer Hopf algebra","authors":"Shingo Kamimoto","doi":"10.3792/pjaa.99.013","DOIUrl":"https://doi.org/10.3792/pjaa.99.013","url":null,"abstract":"We study the resurgence structure of a formal normalization of a certain vector field to the normal form using “mould calculus” developed by J. Écalle. We also describe the resurgence structure of transseries solutions of a nonlinear ordinary differential equation.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135614888","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
Crepant resolution of $mathbf{A}^{4}/A_{4}$ in characteristic 2 特征2中$mathbf{A}^{4}/A_{4}$的渐进解析
4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-11-01 DOI: 10.3792/pjaa.99.014
Linghu Fan
{"title":"Crepant resolution of $mathbf{A}^{4}/A_{4}$ in characteristic 2","authors":"Linghu Fan","doi":"10.3792/pjaa.99.014","DOIUrl":"https://doi.org/10.3792/pjaa.99.014","url":null,"abstract":"In this paper, we construct a crepant resolution for the quotient singularity $mathbf{A}^{4}/A_{4}$ in characteristic 2, where $A_{4}$ is the alternating group of degree 4 with permutation action on $mathbf{A}^{4}$. By computing the Euler number of the crepant resolution, we obtain a new counterexample to an analogous statement of McKay correspondence in positive characteristic.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135615021","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
A note on factorisation patterns of division polynomials of elliptic curves over finite fields 有限域上椭圆曲线除法多项式的因式分解模式注记
4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-10-01 DOI: 10.3792/pjaa.99.011
Josep M. Miret, Daniel Sadornil, Juan Tena, Javier Valera
{"title":"A note on factorisation patterns of division polynomials of elliptic curves over finite fields","authors":"Josep M. Miret, Daniel Sadornil, Juan Tena, Javier Valera","doi":"10.3792/pjaa.99.011","DOIUrl":"https://doi.org/10.3792/pjaa.99.011","url":null,"abstract":"Let $E$ be an elliptic curve defined over a finite field $mathbf{F}_{q}$, $q = p^{d}$, $p > 3$, and a prime number $ell > 3$ such that $q equiv 1 pmod{ell}$ and $ell mid # E(mathbf{F}_{q})$. In this paper we study the possible factorisation patterns over $mathbf{F}_{q}[x]$ of the $ell^{k}$-division polynomials associated to $E$ with $k geq 2$, extending the work of Verdure [6] for $k=1$.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134934890","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
Gosper’s strange series: A new, simplified proof and generalizations 戈斯帕尔的奇怪系列:一个新的，简化的证明和推广
4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-10-01 DOI: 10.3792/pjaa.99.012
John Campbell
{"title":"Gosper’s strange series: A new, simplified proof and generalizations","authors":"John Campbell","doi":"10.3792/pjaa.99.012","DOIUrl":"https://doi.org/10.3792/pjaa.99.012","url":null,"abstract":"In 1977, Gosper introduced a conjectural evaluation for a hypergeometric series that has been described as strange by a number of authors. In 2013, Ebisu proved Gosper’s conjecture using contiguity operators. Subsequently, in 2017, Chu provided another proof of Gosper’s conjecture, using a telescoping argument together with Pfaff’s transformation. In this article, we present a new and simplified proof of Gosper’s conjecture that is inequivalent to the previous proofs due to Ebisu and Chu. Our proof relies on an evaluation technique that was previously given by Campbell and Cantarini and that involves the modified Abel lemma on summation by parts. We also show how this method may be applied to prove generalizations and variants of Gosper’s summation.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134934891","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
Non-purely non-symplectic automorphisms of odd order on $K3$ surfaces K3曲面上奇阶的非纯非辛自同构
IF 0.5 4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-07-31 DOI: 10.3792/pjaa.99.009
Shingo Taki
{"title":"Non-purely non-symplectic automorphisms of odd order on $K3$ surfaces","authors":"Shingo Taki","doi":"10.3792/pjaa.99.009","DOIUrl":"https://doi.org/10.3792/pjaa.99.009","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80447762","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
Notes on a certain local time and excursions of simple symmetric random walks 关于简单对称随机漫步的局部时间和漫游的注释
IF 0.5 4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-07-31 DOI: 10.3792/pjaa.99.010
T. Fujita, N. Yoshida
{"title":"Notes on a certain local time and excursions of simple symmetric random walks","authors":"T. Fujita, N. Yoshida","doi":"10.3792/pjaa.99.010","DOIUrl":"https://doi.org/10.3792/pjaa.99.010","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81355391","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
$q$-Log-concavity and $q$-unimodality of Gaussian polynomials and a problem of Andrews and Newman 高斯多项式的$q$- log -凹凸性和$q$-单模性及Andrews和Newman的一个问题
IF 0.5 4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-05-01 DOI: 10.3792/pjaa.99.007
Shane Chern
{"title":"$q$-Log-concavity and $q$-unimodality of Gaussian polynomials and a problem of Andrews and Newman","authors":"Shane Chern","doi":"10.3792/pjaa.99.007","DOIUrl":"https://doi.org/10.3792/pjaa.99.007","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86991181","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
Proportion of modular forms with transcendental zeros for general levels 一般层次上具有超越零的模形式的比例
IF 0.5 4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-02-10 DOI: 10.3792/pjaa.99.004
D. Choi, Youngmin Lee, Subong Lim, Jaegwang Ryu
{"title":"Proportion of modular forms with transcendental zeros for general levels","authors":"D. Choi, Youngmin Lee, Subong Lim, Jaegwang Ryu","doi":"10.3792/pjaa.99.004","DOIUrl":"https://doi.org/10.3792/pjaa.99.004","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85949206","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
Rational period functions for $Gamma_{0}^{+}(2)$ with poles only in $mathbf{Q}cup {infty}$ 有理周期函数$Gamma_{0}^{+}(2)$只在 $mathbf{Q}cup {infty}$
IF 0.5 4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-01-11 DOI: 10.3792/pjaa.99.002
D. Y. Oh
{"title":"Rational period functions for $Gamma_{0}^{+}(2)$ with poles only in $mathbf{Q}cup {infty}$","authors":"D. Y. Oh","doi":"10.3792/pjaa.99.002","DOIUrl":"https://doi.org/10.3792/pjaa.99.002","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90886104","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
On some arithmetic questions of reductive groups over algebraic extensions of local and global fields 局部域和全局域代数扩展上约化群的若干算术问题
IF 0.5 4区 数学
Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2023-01-11 DOI: 10.3792/pjaa.99.001
N. Q. Thang
{"title":"On some arithmetic questions of reductive groups over algebraic extensions of local and global fields","authors":"N. Q. Thang","doi":"10.3792/pjaa.99.001","DOIUrl":"https://doi.org/10.3792/pjaa.99.001","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85428188","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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