Ramanujan Journal最新文献

{"title":"A remarkable basic hypergeometric identity.","authors":"Christian Krattenthaler, Wadim Zudilin","doi":"10.1007/s11139-024-00994-4","DOIUrl":"https://doi.org/10.1007/s11139-024-00994-4","url":null,"abstract":"<p><p>We give a closed form for <i>quotients</i> of truncated basic hypergeometric series where the base <i>q</i> is evaluated at roots of unity.</p>","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"66 3","pages":"48"},"PeriodicalIF":0.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11785618/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143081377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Explaining unforeseen congruence relationships between PEND and POND partitions via an Atkin-Lehner involution.","authors":"James A Sellers, Nicolas Allen Smoot","doi":"10.1007/s11139-025-01111-9","DOIUrl":"10.1007/s11139-025-01111-9","url":null,"abstract":"<p><p>For the past several years, numerous authors have studied POD and PED partitions from a variety of perspectives. These are integer partitions wherein the odd parts must be distinct (in the case of POD partitions) or the even parts must be distinct (in the case of PED partitions). More recently, Ballantine and Welch were led to consider POND and PEND partitions, which are integer partitions wherein the odd parts <b>cannot</b> be distinct (in the case of POND partitions) or the even parts <b>cannot</b> be distinct (in the case of PEND partitions). Soon after, the first author proved the following results via elementary <i>q</i>-series identities and generating function manipulations, along with mathematical induction: For all <math><mrow><mi>α</mi> <mo>≥</mo> <mn>1</mn></mrow> </math> and all <math><mrow><mi>n</mi> <mo>≥</mo> <mn>0</mn> <mo>,</mo></mrow> </math> <dispformula> <math> <mrow> <mtable> <mtr> <mtd> <mrow><mrow><mspace></mspace> <mtext>pend</mtext> <mspace></mspace></mrow> <mfenced><msup><mn>3</mn> <mrow><mn>2</mn> <mi>α</mi> <mo>+</mo> <mn>1</mn></mrow> </msup> <mi>n</mi> <mo>+</mo> <mfrac><mrow><mn>17</mn> <mo>·</mo> <msup><mn>3</mn> <mrow><mn>2</mn> <mi>α</mi></mrow> </msup> <mo>-</mo> <mn>1</mn></mrow> <mn>8</mn></mfrac> </mfenced> </mrow> </mtd> <mtd><mrow><mo>≡</mo> <mn>0</mn> <mspace></mspace> <mo>(</mo> <mo>mod</mo> <mspace></mspace> <mn>3</mn> <mo>)</mo> <mo>,</mo> <mspace></mspace> <mtext>and</mtext></mrow> </mtd> </mtr> <mtr> <mtd><mrow><mrow></mrow> <mrow><mspace></mspace> <mtext>pond</mtext> <mspace></mspace></mrow> <mfenced><msup><mn>3</mn> <mrow><mn>2</mn> <mi>α</mi> <mo>+</mo> <mn>1</mn></mrow> </msup> <mi>n</mi> <mo>+</mo> <mfrac><mrow><mn>23</mn> <mo>·</mo> <msup><mn>3</mn> <mrow><mn>2</mn> <mi>α</mi></mrow> </msup> <mo>+</mo> <mn>1</mn></mrow> <mn>8</mn></mfrac> </mfenced> </mrow> </mtd> <mtd><mrow><mo>≡</mo> <mn>0</mn> <mspace></mspace> <mo>(</mo> <mo>mod</mo> <mspace></mspace> <mn>3</mn> <mo>)</mo></mrow> </mtd> </mtr> </mtable> </mrow> </math> </dispformula> where <math> <mrow><mrow><mspace></mspace> <mtext>pend</mtext> <mspace></mspace></mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo></mrow> </math> counts the number of PEND partitions of weight <i>n</i> and <math> <mrow><mrow><mspace></mspace> <mtext>pond</mtext> <mspace></mspace></mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo></mrow> </math> counts the number of POND partitions of weight <i>n</i>. In this work, we revisit these families of congruences, and we show a relationship between them via an Atkin-Lehner involution. From this relationship, we can show that, once one of the above families of congruences is known, the other follows immediately.</p>","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"67 3","pages":"60"},"PeriodicalIF":0.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12102003/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144144343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normal distribution of bad reduction.","authors":"Robert J Lemke Oliver, Daniel Loughran, Ari Shnidman","doi":"10.1007/s11139-025-01108-4","DOIUrl":"https://doi.org/10.1007/s11139-025-01108-4","url":null,"abstract":"<p><p>We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, <math><mrow><mn>100</mn> <mo>%</mo></mrow> </math> of curves in these families have, in a precise sense, many such primes.</p>","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"67 3","pages":"52"},"PeriodicalIF":0.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12098207/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144144349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inverses of r-primitive k-normal elements over finite fields","authors":"Mamta Rani, Avnish K. Sharma, Sharwan K. Tiwari, Anupama Panigrahi","doi":"10.1007/s11139-023-00785-3","DOIUrl":"https://doi.org/10.1007/s11139-023-00785-3","url":null,"abstract":"This article studies the existence of elements $$alpha $$ in finite fields $$mathbb {F}_{q^n}$$ such that both $$alpha $$ and its inverse $$alpha ^{-1}$$ are r-primitive and k-normal over $$mathbb {F}_q$$ . We define a characteristic function for the set of k-normal elements and use it to establish a sufficient condition for the existence of the desired pair $$(alpha ,alpha ^{-1})$$ . Moreover, we find that for $$nge 7$$ , there always exists a pair $$(alpha ,alpha ^{-1})$$ of 1-primitive and 1-normal elements in $$mathbb {F}_{q^n}$$ over $$mathbb {F}_q$$ . Additionally, we obtain that for $$n=5,6$$ , if $$textrm{gcd}(q,n)=1$$ , there always exists such a pair in $$mathbb {F}_{q^n}$$ , except for the field $$mathbb {F}_{4^5}$$ .","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"10 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266170","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 a variant of Pillai’s problem with factorials and S-units","authors":"Bernadette Faye, Florian Luca, Volker Ziegler","doi":"10.1007/s11139-023-00787-1","DOIUrl":"https://doi.org/10.1007/s11139-023-00787-1","url":null,"abstract":"Abstract Let S be a finite, fixed set of primes. In this paper, we show that the set of integers c which have at least two representations as a difference between a factorial and an S -unit is finite and effectively computable. In particular, we find all integers that can be written in at least two ways as a difference of a factorial and an S -unit associated with the set of primes $${2,3,5,7}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>7</mml:mn> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> .","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267226","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":"Seesaw identities and theta contractions with generalized theta functions, and restrictions of theta lifts","authors":"Shaul Zemel","doi":"10.1007/s11139-023-00786-2","DOIUrl":"https://doi.org/10.1007/s11139-023-00786-2","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220349","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 algebraic twists with composite moduli","authors":"Yongxiao Lin, Philippe Michel","doi":"10.1007/s11139-023-00789-z","DOIUrl":"https://doi.org/10.1007/s11139-023-00789-z","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994932","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 of the 8-regular partition function","authors":"Giacomo Cherubini, Pietro Mercuri","doi":"10.1007/s11139-023-00784-4","DOIUrl":"https://doi.org/10.1007/s11139-023-00784-4","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"225 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079826","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":"Infinite product representations of some q-series","authors":"Florian Münkel, Lerna Pehlivan, Kenneth S. Williams","doi":"10.1007/s11139-023-00790-6","DOIUrl":"https://doi.org/10.1007/s11139-023-00790-6","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113977","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":"Identities on mex-related partitions","authors":"Jane Y. X. Yang, Li Zhou","doi":"10.1007/s11139-023-00744-y","DOIUrl":"https://doi.org/10.1007/s11139-023-00744-y","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135535696","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}