Kida, Rikuna and Sato [KRS10] developed a classification theory for Brumer's quintic polynomials via Kummer theory arising from associated elliptic curves. We generalize their results to elliptic curves associated to Lecacheux's quintic $F_{20}$-polynomials instead of Brumer's quintic $D_5$-polynomials.
{"title":"On Lecacheux’s family of quintic polynomials","authors":"A. Hoshi, Masakazu Koshiba","doi":"10.3792/pjaa.97.001","DOIUrl":"https://doi.org/10.3792/pjaa.97.001","url":null,"abstract":"Kida, Rikuna and Sato [KRS10] developed a classification theory for Brumer's quintic polynomials via Kummer theory arising from associated elliptic curves. We generalize their results to elliptic curves associated to Lecacheux's quintic $F_{20}$-polynomials instead of Brumer's quintic $D_5$-polynomials.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75589980","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}
: Inspired by Denef-Loeser’s identity of the Euler characteristic with compact supports of the contact loci with the Lefschetz numbers of a complex singularity, we study sheaf cohomology groups of contact loci of complex nondegenerate singularities. Moreover, also for these singularities, we obtain a motivic analogue of Leˆ Du˜ng Tra´ng’s work on a monodromy relation of a complex singularity and its restriction to a generic hyperplane.
受Denef-Loeser关于接触轨迹紧支撑欧拉特征与复奇点Lefschetz数的恒等的启发，我们研究了复非简并奇点接触轨迹的轴上同调群。此外，对于这些奇异点，我们也得到了Le - Du ~ ng Tra´ng关于复奇异点的单调关系及其对一般超平面的限制的一个动力模拟。
{"title":"Contact loci, motivic Milnor fibers of nondegenerate singularities","authors":"Q. Lê, T. Nguyen","doi":"10.3792/pjaa.96.003","DOIUrl":"https://doi.org/10.3792/pjaa.96.003","url":null,"abstract":": Inspired by Denef-Loeser’s identity of the Euler characteristic with compact supports of the contact loci with the Lefschetz numbers of a complex singularity, we study sheaf cohomology groups of contact loci of complex nondegenerate singularities. Moreover, also for these singularities, we obtain a motivic analogue of Leˆ Du˜ng Tra´ng’s work on a monodromy relation of a complex singularity and its restriction to a generic hyperplane.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79504292","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}
We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $Gamma backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $Gamma$) or $Gamma$ is trivial (e.g. Plancherel-type formula for semisimple symmetric spaces).
{"title":"Spectral analysis on pseudo-Riemannian locally symmetric spaces","authors":"Fanny Kassel, Toshiyuki Kobayashi","doi":"10.3792/pjaa.96.013","DOIUrl":"https://doi.org/10.3792/pjaa.96.013","url":null,"abstract":"We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $Gamma backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $Gamma$) or $Gamma$ is trivial (e.g. Plancherel-type formula for semisimple symmetric spaces).","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76660367","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}
: The quasi traveling waves with quenching of u t ¼ u xx þ ð 1 (cid:3) u Þ (cid:3) (cid:2) for (cid:2) 2 2 N are considered. The existence of quasi traveling waves with quenching and their quenching rates are studied by applying the Poincare´ compactification.
:考虑了(cid:2) 2 N的准行波为u t¼u xx þ ð 1 (cid:3) u Þ (cid:3) (cid:2)。应用庞加莱紧化研究了具有淬灭性的准行波的存在性及其淬灭速率。
{"title":"Quasi traveling waves with quenching in a reaction-diffusion equation in the presence of negative powers nonlinearity","authors":"Yutaka Ichida, T. Sakamoto","doi":"10.3792/pjaa.96.001","DOIUrl":"https://doi.org/10.3792/pjaa.96.001","url":null,"abstract":": The quasi traveling waves with quenching of u t ¼ u xx þ ð 1 (cid:3) u Þ (cid:3) (cid:2) for (cid:2) 2 2 N are considered. The existence of quasi traveling waves with quenching and their quenching rates are studied by applying the Poincare´ compactification.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77561085","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}
: A brighter light has freshly been shed upon the second moment of the Prime Geodesic Theorem. We work with such moments in the two and three dimensional hyperbolic spaces. Letting E (cid:2) ð X Þ be the error term arising from counting prime geodesics associated to (cid:2) ¼ PSL 2 ð Z ½ i (cid:2)Þ , the bound E (cid:2) ð X Þ (cid:3) X 3 = 2 þ (cid:2) is proved in a square mean sense. Our second moment bound is the pure counterpart of the work of Balog et al. for (cid:2) ¼ PSL 2 ð Z Þ , and the main innovation entails the delicate analysis of sums of Kloosterman sums. We also infer pointwise bounds from the standpoint of the second moment. Finally, we announce the pointwise bound E (cid:2) ð X Þ (cid:3) X 67 = 42 þ (cid:2) for (cid:2) ¼ PSL 2 ð Z ½ i (cid:2)Þ by an application of the Weyl-type subconvexity.
一束明亮的光刚刚洒在质数测地线定理的第二矩上。我们在二维和三维双曲空间中处理这样的力矩。设E (cid:2) ð X Þ是由计算与(cid:2)¼PSL 2 ð Z½i (cid:2)Þ相关的素数测地线引起的误差项，在平方平均意义上证明了界限E (cid:2) ð X Þ (cid:3) x3 = 2 Þ (cid:2)。我们的第二个矩界是Balog等人对(cid:2)¼PSL 2 ð Z Þ的工作的纯粹对应，主要的创新需要对Kloosterman和的和进行精细的分析。我们还从第二矩的立场推断出点边界。最后，我们通过应用weyl型子凸性，宣布了(cid:2)¼PSL 2 ð Z½i (cid:2)Þ的点界E (cid:2) ð X Þ (cid:3) X 67 = 42 Þ (cid:2)。
{"title":"The second moment for counting prime geodesics","authors":"I. Kaneko","doi":"10.3792/pjaa.96.002","DOIUrl":"https://doi.org/10.3792/pjaa.96.002","url":null,"abstract":": A brighter light has freshly been shed upon the second moment of the Prime Geodesic Theorem. We work with such moments in the two and three dimensional hyperbolic spaces. Letting E (cid:2) ð X Þ be the error term arising from counting prime geodesics associated to (cid:2) ¼ PSL 2 ð Z ½ i (cid:2)Þ , the bound E (cid:2) ð X Þ (cid:3) X 3 = 2 þ (cid:2) is proved in a square mean sense. Our second moment bound is the pure counterpart of the work of Balog et al. for (cid:2) ¼ PSL 2 ð Z Þ , and the main innovation entails the delicate analysis of sums of Kloosterman sums. We also infer pointwise bounds from the standpoint of the second moment. Finally, we announce the pointwise bound E (cid:2) ð X Þ (cid:3) X 67 = 42 þ (cid:2) for (cid:2) ¼ PSL 2 ð Z ½ i (cid:2)Þ by an application of the Weyl-type subconvexity.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84012738","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}
{"title":"On the mod 2 cohomology of the classifying space of the exceptional Lie group $E_{6}$","authors":"Masaki Kameko, Masaki Nakagawa, Tetsu Nishimoto","doi":"10.3792/pjaa.95.91","DOIUrl":"https://doi.org/10.3792/pjaa.95.91","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82078496","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}
In this paper we present critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities concerning the limiting cases of the embedding theorems for Sobolev spaces on stratified groups. Moreover, using the critical Gagliardo-Nirenberg inequality the existence of least energy solutions of the nonlinear Schrodinger type equations can be obtained. We also express the best constant in the critical Gagliardo-Nirenberg inequality in the variational form as well as in terms of the ground state solutions of the corresponding nonlinear subelliptic equations.
{"title":"Limiting cases of Sobolev inequalities on stratified groups","authors":"Michael Ruzhansky, Nurgissa Yessirkegenov","doi":"10.3792/pjaa.95.83","DOIUrl":"https://doi.org/10.3792/pjaa.95.83","url":null,"abstract":"In this paper we present critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities concerning the limiting cases of the embedding theorems for Sobolev spaces on stratified groups. Moreover, using the critical Gagliardo-Nirenberg inequality the existence of least energy solutions of the nonlinear Schrodinger type equations can be obtained. We also express the best constant in the critical Gagliardo-Nirenberg inequality in the variational form as well as in terms of the ground state solutions of the corresponding nonlinear subelliptic equations.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87352773","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}
In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. This article focuses on study, characterization of weaving K-frames in different spaces. Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize woven-ness of K- frames.
{"title":"Characterizations of weaving $K$-frames","authors":"A. Bhandari, Debajit Borah, S. Mukherjee","doi":"10.3792/pjaa.96.008","DOIUrl":"https://doi.org/10.3792/pjaa.96.008","url":null,"abstract":"In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. This article focuses on study, characterization of weaving K-frames in different spaces. Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize woven-ness of K- frames.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72370002","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}
{"title":"Corrigendum to “Real abelian fields satisfying the Hilbert-Speiser condition for some small primes $p$”","authors":"H. Ichimura","doi":"10.3792/PJAA.95.80","DOIUrl":"https://doi.org/10.3792/PJAA.95.80","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84033213","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}
Let G be a real reductive Lie group and H a closed subgroup. T. Kobayashi and T. Oshima established a finiteness criterion of multiplicities of irreducible G-modules occurring in the regular representation C1ðG=HÞ by a geometric condition, referred to as real sphericity, namely, H has an open orbit on the real flag variety G=P . This note discusses a refinement of their theorem by replacing a minimal parabolic subgroup P with a general parabolic subgroup Q of G, where a careful analysis is required because the finiteness of the number of H-orbits on the partial flag variety G=Q is not equivalent to the existence of H-open orbit on G=Q.
{"title":"Relationship between orbit decomposition on the flag varieties and multiplicities of induced representations","authors":"T. Tauchi","doi":"10.3792/PJAA.95.75","DOIUrl":"https://doi.org/10.3792/PJAA.95.75","url":null,"abstract":"Let G be a real reductive Lie group and H a closed subgroup. T. Kobayashi and T. Oshima established a finiteness criterion of multiplicities of irreducible G-modules occurring in the regular representation C1ðG=HÞ by a geometric condition, referred to as real sphericity, namely, H has an open orbit on the real flag variety G=P . This note discusses a refinement of their theorem by replacing a minimal parabolic subgroup P with a general parabolic subgroup Q of G, where a careful analysis is required because the finiteness of the number of H-orbits on the partial flag variety G=Q is not equivalent to the existence of H-open orbit on G=Q.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78940823","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}
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