We prove zero density theorems for Dedekind zeta functions in the vicinity of the line Re s = 1, improving an earlier result of W. Staś.
我们证明了 Re s = 1 直线附近的 Dedekind zeta 函数的零密度定理，改进了 W. Staś早先的一个结果。
{"title":"A Note on the Zeros of the Dedekind Zeta Functions","authors":"János Pintz","doi":"10.1556/314.2024.00009","DOIUrl":"https://doi.org/10.1556/314.2024.00009","url":null,"abstract":"We prove zero density theorems for Dedekind zeta functions in the vicinity of the line Re s = 1, improving an earlier result of W. Staś.","PeriodicalId":486701,"journal":{"name":"Mathematica Pannonica","volume":"9 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141661313","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}
Very recently, the authors in [5] proposed the exponential-type operator connected with and studied its convergence estimates. In the present research, we extend the study and obtain the general form of its 𝑝-th order moment; 𝑝 ∈ ℕ ∪ {0}. Further, we establish the simultaneous approximation for the operator under consideration.
{"title":"Simultaneous Approximation for an Exponential Operator Connected with x4/3","authors":"Anjali, Vijay Gupta","doi":"10.1556/314.2024.00007","DOIUrl":"https://doi.org/10.1556/314.2024.00007","url":null,"abstract":"Very recently, the authors in [5] proposed the exponential-type operator connected with and studied its convergence estimates. In the present research, we extend the study and obtain the general form of its 𝑝-th order moment; 𝑝 ∈ ℕ ∪ {0}. Further, we establish the simultaneous approximation for the operator under consideration.","PeriodicalId":486701,"journal":{"name":"Mathematica Pannonica","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140674909","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}
We present examples of multiplicative semigroups of positive reals (Beurling’s generalized integers) with gaps bounded from below.
我们举例说明了正实数（贝林广义整数）的乘法半群，其间隙自下而上是有界的。
{"title":"Beurling-Integers with Lacunarity","authors":"Imre Z. Ruzsa","doi":"10.1556/314.2024.00002","DOIUrl":"https://doi.org/10.1556/314.2024.00002","url":null,"abstract":"We present examples of multiplicative semigroups of positive reals (Beurling’s generalized integers) with gaps bounded from below.","PeriodicalId":486701,"journal":{"name":"Mathematica Pannonica","volume":"34 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139687646","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}
Let 𝑓 be a normalized primitive cusp form of even integral weight for the full modular group Γ = 𝑆𝐿(2, ℤ). In this paper, we investigate upper bounds for the error terms related to the average behavior of Fourier coefficients 𝜆𝑓 ⊗𝑓 ⊗⋯⊗𝑙𝑓 (𝑛) of 𝑙-fold product 𝐿-functions, where 𝑓 ⊗ 𝑓 ⊗ ⋯ ⊗𝑙 𝑓 denotes the 𝑙-fold product of 𝑓. These results improves and generalizes the recent developments of Venkatasubbareddy and Sankaranarayanan [41]. We also provide some other similar results related to the error terms of general product 𝐿-functions.
{"title":"On the Fourier Coefficients for General Product 𝐿-Functions","authors":"Guodong Hua","doi":"10.1556/314.2024.00003","DOIUrl":"https://doi.org/10.1556/314.2024.00003","url":null,"abstract":"Let 𝑓 be a normalized primitive cusp form of even integral weight for the full modular group Γ = 𝑆𝐿(2, ℤ). In this paper, we investigate upper bounds for the error terms related to the average behavior of Fourier coefficients 𝜆𝑓 ⊗𝑓 ⊗⋯⊗𝑙𝑓 (𝑛) of 𝑙-fold product 𝐿-functions, where 𝑓 ⊗ 𝑓 ⊗ ⋯ ⊗𝑙 𝑓 denotes the 𝑙-fold product of 𝑓. These results improves and generalizes the recent developments of Venkatasubbareddy and Sankaranarayanan [41]. We also provide some other similar results related to the error terms of general product 𝐿-functions.","PeriodicalId":486701,"journal":{"name":"Mathematica Pannonica","volume":"38 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139686481","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}
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