International Journal of Number Theory最新文献

{"title":"p-Adic hypergeometric functions and the trace of Frobenius of elliptic curves","authors":"Rupam Barman, Sulakashna","doi":"10.1142/s1793042124501276","DOIUrl":"https://doi.org/10.1142/s1793042124501276","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141652554","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":"Translation functors for locally analytic representations","authors":"Akash Jena, Aranya Lahiri, Matthias Strauch","doi":"10.1142/s1793042124501252","DOIUrl":"https://doi.org/10.1142/s1793042124501252","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653197","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":"Almost prime triples and Chen's theorem","authors":"Li Zhu","doi":"10.1142/s1793042125500071","DOIUrl":"https://doi.org/10.1142/s1793042125500071","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653739","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 the Shintani lifting of integral weight modular forms to half-integral weight modular forms","authors":"Di Zhang","doi":"10.1142/s1793042125500010","DOIUrl":"https://doi.org/10.1142/s1793042125500010","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141654839","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":"Congruences for partial sums of the generating series for 3kk","authors":"Sandro Mattarei, R. Tauraso","doi":"10.1142/s1793042125500125","DOIUrl":"https://doi.org/10.1142/s1793042125500125","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141652494","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 integers of the form p + 2a2 + 2b2","authors":"Ji-Zhen Xu, Yong-Gao Chen","doi":"10.1142/s1793042125500083","DOIUrl":"https://doi.org/10.1142/s1793042125500083","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141653534","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":"Pairs of cyclic cubic units with rational difference","authors":"Toru Komatsu","doi":"10.1142/s1793042125500034","DOIUrl":"https://doi.org/10.1142/s1793042125500034","url":null,"abstract":"","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141655067","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":"Riemann hypothesis for period polynomials for cusp forms on Γ0(N)","authors":"SoYoung Choi","doi":"10.1142/s1793042124500982","DOIUrl":"https://doi.org/10.1142/s1793042124500982","url":null,"abstract":"<p>We prove that for even integer <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi>k</mi></math></span><span></span>, almost all of zeros of the period polynomial associated to a cusp form of weight <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi>k</mi></math></span><span></span> on <span><math altimg=\"eq-00005.gif\" display=\"inline\"><msub><mrow><mi mathvariant=\"normal\">Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy=\"false\">(</mo><mi>N</mi><mo stretchy=\"false\">)</mo></math></span><span></span> are on the circle <span><math altimg=\"eq-00006.gif\" display=\"inline\"><mo>|</mo><mi>z</mi><mo>|</mo><mo>=</mo><mn>1</mn><mo stretchy=\"false\">/</mo><msqrt><mrow><mi>N</mi></mrow></msqrt></math></span><span></span> under some conditions.</p>","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253809","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":"Lehmer-type bounds and counting rational points of bounded heights on Abelian varieties","authors":"Narasimha Kumar, Satyabrat Sahoo","doi":"10.1142/s1793042124501045","DOIUrl":"https://doi.org/10.1142/s1793042124501045","url":null,"abstract":"<p>In this paper, we study Lehmer-type bounds for the Néron–Tate height of <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mover accent=\"true\"><mrow><mi>K</mi></mrow><mo>̄</mo></mover></math></span><span></span>-points on abelian varieties <span><math altimg=\"eq-00002.gif\" display=\"inline\"><mi>A</mi></math></span><span></span> over number fields <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi>K</mi></math></span><span></span>. Then, we estimate the number of <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi>K</mi></math></span><span></span>-rational points on <span><math altimg=\"eq-00005.gif\" display=\"inline\"><mi>A</mi></math></span><span></span> with Néron–Tate height <span><math altimg=\"eq-00006.gif\" display=\"inline\"><mo>≤</mo><mo>log</mo><mi>B</mi></math></span><span></span> for <span><math altimg=\"eq-00007.gif\" display=\"inline\"><mi>B</mi><mo>≫</mo><mn>0</mn></math></span><span></span>. This estimate involves a constant <span><math altimg=\"eq-00008.gif\" display=\"inline\"><mi>C</mi></math></span><span></span>, which is not explicit. However, for elliptic curves and the product of elliptic curves over <span><math altimg=\"eq-00009.gif\" display=\"inline\"><mi>K</mi></math></span><span></span>, we make the constant explicitly computable.</p>","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253929","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":"Arithmetic progressions in polynomial orbits","authors":"Mohammad Sadek, Mohamed Wafik, Tuğba Yesin","doi":"10.1142/s1793042124500970","DOIUrl":"https://doi.org/10.1142/s1793042124500970","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\"><mi>f</mi></math></span><span></span> be a polynomial with integer coefficients whose degree is at least 2. We consider the problem of covering the orbit <span><math altimg=\"eq-00002.gif\" display=\"inline\"><msub><mrow><mo>Orb</mo></mrow><mrow><mi>f</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo stretchy=\"false\">{</mo><mi>t</mi><mo>,</mo><mi>f</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo>,</mo><mi>f</mi><mo stretchy=\"false\">(</mo><mi>f</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">)</mo><mo>,</mo><mo>…</mo><mo stretchy=\"false\">}</mo></math></span><span></span>, where <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi>t</mi></math></span><span></span> is an integer, using arithmetic progressions each of which contains <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi>t</mi></math></span><span></span>. Fixing an integer <span><math altimg=\"eq-00005.gif\" display=\"inline\"><mi>k</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, we prove that it is impossible to cover <span><math altimg=\"eq-00006.gif\" display=\"inline\"><msub><mrow><mo>Orb</mo></mrow><mrow><mi>f</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> using <span><math altimg=\"eq-00007.gif\" display=\"inline\"><mi>k</mi></math></span><span></span> such arithmetic progressions unless <span><math altimg=\"eq-00008.gif\" display=\"inline\"><msub><mrow><mo>Orb</mo></mrow><mrow><mi>f</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is contained in one of these progressions. In fact, we show that the relative density of terms covered by <span><math altimg=\"eq-00009.gif\" display=\"inline\"><mi>k</mi></math></span><span></span> such arithmetic progressions in <span><math altimg=\"eq-00010.gif\" display=\"inline\"><msub><mrow><mo>Orb</mo></mrow><mrow><mi>f</mi></mrow></msub><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is uniformly bounded from above by a bound that depends solely on <span><math altimg=\"eq-00011.gif\" display=\"inline\"><mi>k</mi></math></span><span></span>. In addition, the latter relative density can be made as close as desired to <span><math altimg=\"eq-00012.gif\" display=\"inline\"><mn>1</mn></math></span><span></span> by an appropriate choice of <span><math altimg=\"eq-00013.gif\" display=\"inline\"><mi>k</mi></math></span><span></span> arithmetic progressions containing <span><math altimg=\"eq-00014.gif\" display=\"inline\"><mi>t</mi></math></span><span></span> if <span><math altimg=\"eq-00015.gif\" display=\"inline\"><mi>k</mi></math></span><span></span> is allowed to be large enough.</p>","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253805","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}