Ramanujan Journal最新文献

{"title":"On restricted approximation measures of Jacobi’s triple product","authors":"Leena Leinonen, Marko Leinonen","doi":"10.1007/s11139-023-00776-4","DOIUrl":"https://doi.org/10.1007/s11139-023-00776-4","url":null,"abstract":"Abstract We obtain rational approximations for Jacobi’s triple product $$begin{aligned} Pi _q(t):= prod _{m=1}^infty (1-q^{2m})(1+q^{2m-1}t)(1+q^{2m-1}t^{-1}), end{aligned}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msub> <mml:mi>Π</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>:</mml:mo> <mml:mo>=</mml:mo> <mml:munderover> <mml:mo>∏</mml:mo> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>∞</mml:mi> </mml:munderover> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>q</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>q</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>q</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> </mml:mrow> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mrow> </mml:math> when $$t=a/bin {mathbb {Q}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mi>a</mml:mi> <mml:mo>/</mml:mo> <mml:mi>b</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Q</mml:mi> </mml:mrow> </mml:math> is non-zero and $$q=1/d$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:math> with $$din {mathbb {Z}}{setminus }{0, pm 1 }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Z</mml:mi> <mml:mo></mml:mo> <mml:mo>{</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> . Especially we give effective and restricted approximation for the values of Jacobi’s triple product and for the values of Euler’s infinite product.","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135980836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypergeometric functions over finite fields","authors":"Noriyuki Otsubo","doi":"10.1007/s11139-023-00777-3","DOIUrl":"https://doi.org/10.1007/s11139-023-00777-3","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Additive evaluations of the number of divisors","authors":"Mircea Merca","doi":"10.1007/s11139-023-00773-7","DOIUrl":"https://doi.org/10.1007/s11139-023-00773-7","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135938886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some problems about friable numbers in Piatetski-Shapiro sequence","authors":"Wenbin Zhu","doi":"10.1007/s11139-023-00774-6","DOIUrl":"https://doi.org/10.1007/s11139-023-00774-6","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42642499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A closed-form expression for the Euler–Kronecker constant of a quadratic field","authors":"Suraj Singh Khurana","doi":"10.1007/s11139-023-00772-8","DOIUrl":"https://doi.org/10.1007/s11139-023-00772-8","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45131582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lower bounds for the house in some radical extensions","authors":"Francesco Amoroso","doi":"10.1007/s11139-023-00771-9","DOIUrl":"https://doi.org/10.1007/s11139-023-00771-9","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41527292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Euler sums of generalized alternating hyperharmonic numbers II","authors":"Rusen Li","doi":"10.1007/s11139-023-00761-x","DOIUrl":"https://doi.org/10.1007/s11139-023-00761-x","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134951875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parity bias for the partitions with bounded number of appearances of the part of size 1","authors":"Byungchan Kim, Eunmi Kim","doi":"10.1007/s11139-023-00775-5","DOIUrl":"https://doi.org/10.1007/s11139-023-00775-5","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41778789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrepancy estimates for some linear generalized monomials at prime arguments","authors":"C. G. K. Babu, Anirban Mukhopadhyay, G. K. Viswanadham","doi":"10.1007/s11139-023-00767-5","DOIUrl":"https://doi.org/10.1007/s11139-023-00767-5","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41319534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact values and lower bounds on the n-color weak Schur numbers for n=2,3documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document","authors":"T. Ahmed, L. Boza, M. P. Revuelta, M. I. Sanz","doi":"10.1007/s11139-023-00760-y","DOIUrl":"https://doi.org/10.1007/s11139-023-00760-y","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"62 1","pages":"347 - 363"},"PeriodicalIF":0.7,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47709222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}