Pub Date : 2023-09-15DOI: 10.1007/s11139-023-00783-5
Yan Fan, Eric H. Liu, Ernest X. W. Xia
{"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":null,"pages":null},"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}
Pub Date : 2023-09-12DOI: 10.1007/s11139-023-00778-2
Bruce C. Berndt, Sun Kim, Alexandru Zaharescu
{"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":null,"pages":null},"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}
Pub Date : 2023-09-11DOI: 10.1007/s11139-023-00779-1
Sebastián Carrillo Santana
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.
{"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":null,"pages":null},"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}
Pub Date : 2023-09-11DOI: 10.1007/s11139-023-00776-4
Leena Leinonen, Marko Leinonen
Abstract We obtain rational approximations for Jacobi’s triple product $$begin{aligned} Pi _q(t):= prod _{m=1}^infty (1-q^{2m})(1+q^{2m-1}t)(1+q^{2m-1}t^{-1}), end{aligned}$$ Πq(t):=∏m=1∞(1-q2m)(1+q2m-1t)(1+q2m-1t-1), when $$t=a/bin {mathbb {Q}}$$ t=a/b∈Q is non-zero and $$q=1/d$$ q=1/d with $$din {mathbb {Z}}{setminus }{0, pm 1 }$$ d∈Z{0,±1} . Especially we give effective and restricted approximation for the values of Jacobi’s triple product and for the values of Euler’s infinite product.
当$$t=a/bin {mathbb {Q}}$$ t = a / b∈q非零，$$q=1/d$$ q = 1 / d, $$din {mathbb {Z}}{setminus }{0, pm 1 }$$ d∈Z 1时，得到Jacobi三重积$$begin{aligned} Pi _q(t):= prod _{m=1}^infty (1-q^{2m})(1+q^{2m-1}t)(1+q^{2m-1}t^{-1}), end{aligned}$$ Π q (t): =∏m = 1∞(1 - q 2 m) (1 + q 2 m - 1 t) (1 + q 2 m - 1 t) (1 + q 2 m - 1 t - 1)的有理逼近。特别给出了雅可比三重积和欧拉无穷积的有效和有限近似。{}
{"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":null,"pages":null},"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}
Pub Date : 2023-09-11DOI: 10.1007/s11139-023-00773-7
Mircea Merca
{"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":null,"pages":null},"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}
Pub Date : 2023-09-04DOI: 10.1007/s11139-023-00772-8
Suraj Singh Khurana
{"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":null,"pages":null},"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}
Pub Date : 2023-09-02DOI: 10.1007/s11139-023-00771-9
Francesco Amoroso
{"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":null,"pages":null},"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}
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