Ramanujan Journal最新文献

{"title":"Some identities on Beck’s partition statistics","authors":"Yongqiang Chen, Jing Jin, Olivia X. M. Yao","doi":"10.1007/s11139-023-00781-7","DOIUrl":"https://doi.org/10.1007/s11139-023-00781-7","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134961156","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":"Alternating multiple T-values: weighted sums, duality, and dimension conjecture","authors":"Ce Xu, Jianqiang Zhao","doi":"10.1007/s11139-023-00782-6","DOIUrl":"https://doi.org/10.1007/s11139-023-00782-6","url":null,"abstract":"In this paper, we define some weighted sums of the alternating multiple T-values (AMTVs) and study several duality formulas for them. Then we introduce the alternating version of the convoluted T-values and Kaneko–Tsumura $$psi $$ -function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $$mathbb {Q}$$ -vector space generated by the AMTVs of any fixed weight w and provide some evidence for the conjecture that their dimensions $${d_w}_{wge 1}$$ form the tribonacci sequence 1, 2, 4, 7, 13, ....","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134904247","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":"Composition-theoretic series in partition theory","authors":"Robert Schneider, Andrew V. Sills","doi":"10.1007/s11139-023-00780-8","DOIUrl":"https://doi.org/10.1007/s11139-023-00780-8","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437152","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":"Inequalities for the $$M_2$$-rank modulo 12 of partitions without repeated odd parts","authors":"Yan Fan, Eric H. Liu, Ernest X. W. Xia","doi":"10.1007/s11139-023-00783-5","DOIUrl":"https://doi.org/10.1007/s11139-023-00783-5","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"204 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436255","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":"Finite trigonometric sums arising from Ramanujan’s theta functions","authors":"Bruce C. Berndt, Sun Kim, Alexandru Zaharescu","doi":"10.1007/s11139-023-00778-2","DOIUrl":"https://doi.org/10.1007/s11139-023-00778-2","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135826631","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":"The first negative Fourier coefficient of an Eisenstein series newform","authors":"Sebastián Carrillo Santana","doi":"10.1007/s11139-023-00779-1","DOIUrl":"https://doi.org/10.1007/s11139-023-00779-1","url":null,"abstract":"Abstract There have been a number of papers on statistical questions concerning the sign changes of Fourier coefficients of newforms. In one such paper, Linowitz and Thompson gave a conjecture describing when, on average, the first negative sign of the Fourier coefficients of an Eisenstein series newform occurs. In this paper, we correct their conjecture and prove the corrected version.","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"22 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":"135979468","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":"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}