Pub Date : 2023-05-15DOI: 10.21136/cmj.2023.0236-22
Gastón Beltritti, Stefania Demaria, G. Giubergia, F. Mazzone
{"title":"The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations","authors":"Gastón Beltritti, Stefania Demaria, G. Giubergia, F. Mazzone","doi":"10.21136/cmj.2023.0236-22","DOIUrl":"https://doi.org/10.21136/cmj.2023.0236-22","url":null,"abstract":"","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42815974","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}
Pub Date : 2023-04-27DOI: 10.21136/cmj.2023.0511-22
Yongjun Xu, Xin Zhang
{"title":"Symmetries in connected graded algebras and their PBW-deformations","authors":"Yongjun Xu, Xin Zhang","doi":"10.21136/cmj.2023.0511-22","DOIUrl":"https://doi.org/10.21136/cmj.2023.0511-22","url":null,"abstract":"","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41366128","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}
Pub Date : 2023-04-27DOI: 10.21136/CMJ.2023.0364-22
M. Ram
For any square-free positive integer m ≡ 10 (mod 16) with m ⩾ 26, we prove that the class number of the real cyclotomic field ℚ(ζ4m +ζ4m−1) is greater than 1, where ζ4m is a primitive 4mth root of unity.
{"title":"On the class number of the maximal real subfields of a family of cyclotomic fields","authors":"M. Ram","doi":"10.21136/CMJ.2023.0364-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0364-22","url":null,"abstract":"For any square-free positive integer m ≡ 10 (mod 16) with m ⩾ 26, we prove that the class number of the real cyclotomic field ℚ(ζ4m +ζ4m−1) is greater than 1, where ζ4m is a primitive 4mth root of unity.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"937 - 940"},"PeriodicalIF":0.5,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42565585","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}
Pub Date : 2023-04-27DOI: 10.21136/CMJ.2023.0348-22
Anubhav Sharma, A. Sankaranarayanan
We investigate the average behavior of the nth normalized Fourier coefficients of the jth (j ≽ 2 be any fixed integer) symmetric power L-function (i.e., L(s,symjf)), attached to a primitive holomorphic cusp form f of weight k for the full modular group SL(2,ℤ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$SL(2,mathbb{Z})$$end{document} over certain sequences of positive integers. Precisely, we prove an asymptotic formula with an error term for the sum Sj∗:=∑a12+a22+a32+a42+a52+a62⩽x(a1,a2,a3,a4,a5,a6)∈ℤ6λsymjf2(a12+a22+a32+a42+a52+a62),documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S_j^ *: = sumlimits_{matrix{{a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 + a_6^2x} cr {({a_1},{a_2},{a_3},{a_4},{a_5},{a_6}) in {mathbb{Z}^6}} cr}} {lambda _{{rm{sy}}{{rm{m}}^j}f}^2(a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 + a_6^2),} $$end{document} where x is sufficiently large, and L(s,symjf):=∑n=1∞λsymjf(n)ns.documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L(s,{rm{sy}}{{rm{m}}^j}f): = sumlimits_{n = 1}^infty {{{{lambda _{{rm{sy}}{{rm{m}}^j}f}}(n)} over {{n^s}}}}.$$end{document} When j = 2, the error term which we obtain improves the earlier known result.
我们研究了全模群SL（2，ℤ)documentclass[12pt]｛minimal｝ usepackage｛amsmath｝ use package｛｛wasysym｝usepackage{amsfonts} usepackage{amssymb｝ userpackage{amsbsy｝usepackage{mathrsfs｝ user package{upgek｝setlength｛doddsedmargin｝｛-69pt｝ begin｛document｝$$SL（2，mathbb｛Z｝）$$end｛document｝在某些正整数序列上。确切地说，我们证明了一个渐近公式，其和Sj＊的误差项为：=∑a12+a22+a32+a42+a52+a62⩽x（a1，a2，a3，a4，a5，a6）∈ℤ6λsymjf2（a12+a22+a32+a42+a52+a62），documentclass[12pt]｛minimum｝ usepackage｛amsmath｝ use package｛S wasysym｝ usapackage{amsfonts｝ userpackage｛｛amssymb｝ user package{amsbsy｝usepackage{mathrsfs｝use package{upgeek｝setlength｛doddsidemargin｝｛-69pt｝ begin｛document｝$S_j^*：=sumlimits_{matrix｛a_1^2+a_2^2+a_3^2+a_1^2+a_5^2+a_ 6^2 x｝cr｛（｛a_2，｛aa2｝，｛a_3｝，｛a_2｝，｝a_5｝，{a_6｝）在｛mathbb｛Z｝^6｝cr｝｝中｛｛rm｛m｝｝^j｝f｝^2（a_1^2+a_2^2+a_3^2+a_1^2），｝$end｛document｝其中x足够大，L（s，symjf）：=∑n=1∞λsymjf（n）ns。documentclass[12pt]｛minimal｝ usepackage｛amsmath｝ use package｛｛wasysym｝usepackage{amsfonts｝ userpackage{amssymb｝ user package{hamsbsy｝usepackage{mathrsfs｝usepackage｛upgek｝setlength｛doddsedmargin｝｛-69pt｝ begin｛document｝$L m｝^j｝f｝｝（n）｝在｛｛n^s｝｝$$end｛document｝当j＝2时，我们获得的误差项改进了先前已知的结果。
{"title":"On the average behavior of the Fourier coefficients of jth symmetric power L-function over certain sequences of positive integers","authors":"Anubhav Sharma, A. Sankaranarayanan","doi":"10.21136/CMJ.2023.0348-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0348-22","url":null,"abstract":"We investigate the average behavior of the nth normalized Fourier coefficients of the jth (j ≽ 2 be any fixed integer) symmetric power L-function (i.e., L(s,symjf)), attached to a primitive holomorphic cusp form f of weight k for the full modular group SL(2,ℤ)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$SL(2,mathbb{Z})$$end{document} over certain sequences of positive integers. Precisely, we prove an asymptotic formula with an error term for the sum Sj∗:=∑a12+a22+a32+a42+a52+a62⩽x(a1,a2,a3,a4,a5,a6)∈ℤ6λsymjf2(a12+a22+a32+a42+a52+a62),documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$S_j^ *: = sumlimits_{matrix{{a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 + a_6^2x} cr {({a_1},{a_2},{a_3},{a_4},{a_5},{a_6}) in {mathbb{Z}^6}} cr}} {lambda _{{rm{sy}}{{rm{m}}^j}f}^2(a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2 + a_6^2),} $$end{document} where x is sufficiently large, and L(s,symjf):=∑n=1∞λsymjf(n)ns.documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L(s,{rm{sy}}{{rm{m}}^j}f): = sumlimits_{n = 1}^infty {{{{lambda _{{rm{sy}}{{rm{m}}^j}f}}(n)} over {{n^s}}}}.$$end{document} When j = 2, the error term which we obtain improves the earlier known result.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"885 - 901"},"PeriodicalIF":0.5,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43217567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-13DOI: 10.21136/CMJ.2023.0351-22
L. Mao
Let R ⋉ M be a trivial extension of a ring R by an R-R-bimodule M such that MR, RM, (R, 0)R⋉ M and R⋉M(R, 0) have finite flat dimensions. We prove that (X, α) is a Ding projective left R ⋉ M-module if and only if the sequence M⊗RM⊗RX→M⊗αM⊗RX→αXdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$M{otimes _R}M{otimes _R}Xmathop to limits^{M otimes alpha} M{otimes _R}Xmathop to limits^alpha X$$end{document} is exact and coker(α) is a Ding projective left R-module. Analogously, we explicitly describe Ding injective R ⋉ M-modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.
{"title":"Ding projective and Ding injective modules over trivial ring extensions","authors":"L. Mao","doi":"10.21136/CMJ.2023.0351-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0351-22","url":null,"abstract":"Let R ⋉ M be a trivial extension of a ring R by an R-R-bimodule M such that MR, RM, (R, 0)R⋉ M and R⋉M(R, 0) have finite flat dimensions. We prove that (X, α) is a Ding projective left R ⋉ M-module if and only if the sequence M⊗RM⊗RX→M⊗αM⊗RX→αXdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$M{otimes _R}M{otimes _R}Xmathop to limits^{M otimes alpha} M{otimes _R}Xmathop to limits^alpha X$$end{document} is exact and coker(α) is a Ding projective left R-module. Analogously, we explicitly describe Ding injective R ⋉ M-modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"903 - 919"},"PeriodicalIF":0.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48649512","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}
Pub Date : 2023-03-24DOI: 10.21136/cmj.2023.0437-22
K. Tvrdá, P. Novotný
{"title":"Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives","authors":"K. Tvrdá, P. Novotný","doi":"10.21136/cmj.2023.0437-22","DOIUrl":"https://doi.org/10.21136/cmj.2023.0437-22","url":null,"abstract":"","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48694248","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}
Pub Date : 2023-03-22DOI: 10.21136/cmj.2023.0257-22
J. H. Arredondo, Manuel Bernal, M. G. Morales
{"title":"A necessary condition for HK-integrability of the Fourier sine transform function","authors":"J. H. Arredondo, Manuel Bernal, M. G. Morales","doi":"10.21136/cmj.2023.0257-22","DOIUrl":"https://doi.org/10.21136/cmj.2023.0257-22","url":null,"abstract":"","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47690220","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}
Pub Date : 2023-03-20DOI: 10.21136/CMJ.2023.0116-22
G. Lu, Dinghuai Wang
We study the mapping property of the commutator of Hardy-Littlewood maximal function on Triebel-Lizorkin spaces. Also, some new characterizations of the Lipschitz spaces are given.
{"title":"Characterizations of commutators of the Hardy-Littlewood maximal function on Triebel-Lizorkin spaces","authors":"G. Lu, Dinghuai Wang","doi":"10.21136/CMJ.2023.0116-22","DOIUrl":"https://doi.org/10.21136/CMJ.2023.0116-22","url":null,"abstract":"We study the mapping property of the commutator of Hardy-Littlewood maximal function on Triebel-Lizorkin spaces. Also, some new characterizations of the Lipschitz spaces are given.","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"73 1","pages":"513 - 524"},"PeriodicalIF":0.5,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44864172","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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