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The Okada space and vanishing of ${L(1,{f})}$ ${L(1，{f})}$的Okada空间及其消失
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1952
M. Murty, Siddhi Pathak
{"title":"The Okada space and vanishing of ${L(1,{f})}$","authors":"M. Murty, Siddhi Pathak","doi":"10.7169/facm/1952","DOIUrl":"https://doi.org/10.7169/facm/1952","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42035749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 derivative of iterations of the Minkowski question mark function at special points 闵可夫斯基问号函数在特殊点上的迭代导数
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1966
N. Shulga
{"title":"On the derivative of iterations of the Minkowski question mark function at special points","authors":"N. Shulga","doi":"10.7169/facm/1966","DOIUrl":"https://doi.org/10.7169/facm/1966","url":null,"abstract":"For the Minkowski question mark function ?(x) we consider derivative of the function fn(x) = ?(?(...? } {{ } n times (x))). Apart from obvious cases (rational numbers for example) it is non-trivial to find explicit examples of numbers x for which f ′ n (x) = 0. In this paper we present a set of irrational numbers, such that for every element x0 of this set and for any n ∈ Z+ one has f ′ n (x0) = 0.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47218659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gauss sums and the maximum cliquesin generalized Paley graphs of square order 平方阶广义Paley图的Gauss和与最大群
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1981
Chi Hoi Yip
{"title":"Gauss sums and the maximum cliquesin generalized Paley graphs of square order","authors":"Chi Hoi Yip","doi":"10.7169/facm/1981","DOIUrl":"https://doi.org/10.7169/facm/1981","url":null,"abstract":"Let GP (q, d) be the d-Paley graph defined on the finite field Fq . It is notoriously difficult to improve the trivial upper bound √ q on the clique number of GP (q, d). In this paper, we investigate the connection between Gauss sums over a finite field and the maximum cliques of their corresponding generalized Paley graphs. We show that the trivial upper bound on the clique number of GP (q, d) is tight if and only if d | (√q + 1), which strengthens the previous related results by Broere-Döman-Ridley and Schneider-Silva. We also obtain a new simple proof of Stickelberger’s theorem on evaluating semi-primitive Gauss sums.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44025836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers 正指数多变量Arakawa Kaneko-zeta函数的解析延拓及其在正整数上的值
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1974
K. Ito
{"title":"Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers","authors":"K. Ito","doi":"10.7169/facm/1974","DOIUrl":"https://doi.org/10.7169/facm/1974","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49466735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Asymptotic behavior of Bernoulli-Dunkland Euler-Dunkl polynomials and their zeros Bernoulli-Dunkland Euler-Dunkl多项式及其零的渐近性质
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1968
J. M. Ceniceros, J. Varona
{"title":"Asymptotic behavior of Bernoulli-Dunkland Euler-Dunkl polynomials and their zeros","authors":"J. M. Ceniceros, J. Varona","doi":"10.7169/facm/1968","DOIUrl":"https://doi.org/10.7169/facm/1968","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44295523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On a generalization of the Euler totient function 欧拉全等函数的推广
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/FACM/1917
W. Zhai
{"title":"On a generalization of the Euler totient function","authors":"W. Zhai","doi":"10.7169/FACM/1917","DOIUrl":"https://doi.org/10.7169/FACM/1917","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42036478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Heat operators on modular and quasimodular polynomials 模和准模多项式上的热算子
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1978
Min Ho Lee
{"title":"Heat operators on modular and quasimodular polynomials","authors":"Min Ho Lee","doi":"10.7169/facm/1978","DOIUrl":"https://doi.org/10.7169/facm/1978","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47411051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
${P}$-adic approximation of Dedekind sumsin function fields Dedekind sumsin函数域的${P}$adic近似
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1961
Y. Hamahata
{"title":"${P}$-adic approximation of Dedekind sumsin function fields","authors":"Y. Hamahata","doi":"10.7169/facm/1961","DOIUrl":"https://doi.org/10.7169/facm/1961","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41449406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the consecutive prime divisors of an integer 关于整数的连续素数
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1922
J. Koninck, Imre Kátai Imre Kátai
{"title":"On the consecutive prime divisors of an integer","authors":"J. Koninck, Imre Kátai Imre Kátai","doi":"10.7169/facm/1922","DOIUrl":"https://doi.org/10.7169/facm/1922","url":null,"abstract":"Paul Erd˝os, Janos Galambos and others have studied the relative size of the consecutive prime divisors of an integer. Here, we further extend this study by examining the distribution of the consecutive neighbour spacings between the prime divisors p 1 ( n ) < p 2 ( n ) < · · · < p r ( n ) of a typical integer n ≥ 2. In particular, setting γ j ( n ) := log p j ( n ) / log p j +1 ( n ) for j = 1 , 2 , . . . , r − 1 and, for any λ ∈ (0 , 1], introducing U λ ( n ) := # { j ∈ { 1 , 2 , . . . , r − 1 } : γ j ( n ) < λ } , we establish the mean value of U λ ( n ) and prove that U λ ( n ) /r ∼ λ for almost all integers n ≥ 2. We also examine the shifted prime version of these two results and study other related functions.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42847513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Calculating “small” solutions of inhomogeneous relative Thue inequalities 计算非齐次相对Thue不等式的“小”解
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1876
Istv'an Ga'al
{"title":"Calculating “small” solutions of inhomogeneous relative Thue inequalities","authors":"Istv'an Ga'al","doi":"10.7169/facm/1876","DOIUrl":"https://doi.org/10.7169/facm/1876","url":null,"abstract":"Thue equations and their relative and inhomogeneous extensions are well known in the literature. There exist methods, usually tedious methods, for the complete resolution of these equations. On the other hand our experiences show that such equations usually do not have extremely large solutions. Therefore in several applications it is useful to have a fast algorithm to calculate the\"small\"solutions of these equations. Under\"small\"solutions we mean the solutions, say, with absolute values or sizes $leq 10^{100}$. Such algorithms were formerly constructed for Thue equations, relative Thue equations. The relative and inhomogeneous Thue equations have applications in solving index form equations and certain resultant form equations. It is also known that certain\"totally real\"relative Thue equations can be reduced to absolute Thue equations (equations over $Bbb Z$). As a common generalization of the above results, in our paper we develop a fast algorithm for calculating\"small\"solutions (say with sizes $leq 10^{100}$) of inhomogeneous relative Thue equations, more exactly of certain inequalities that generalize those equations. We shall show that in the\"totally real\"case these can similarly be reduced to absolute inhomogeneous Thue inequalities. We also give an application to solving certain resultant equations in the relative case.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48913708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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