In this paper we give new estimates for integrals involving some arithmetic functions defined over prime numbers. The main focus here is on the prime counting function $pi(x)$ and the Chebyshev $vartheta$-function. Some of these estimates depend on the correctness of the Riemann hypothesis on the nontrivial zeros of the Riemann zeta function $zeta(s)$.
{"title":"New estimates for some integrals of functions defined over primes","authors":"Christian Axler","doi":"10.7169/facm/2049","DOIUrl":"https://doi.org/10.7169/facm/2049","url":null,"abstract":"In this paper we give new estimates for integrals involving some arithmetic functions defined over prime numbers. The main focus here is on the prime counting function $pi(x)$ and the Chebyshev $vartheta$-function. Some of these estimates depend on the correctness of the Riemann hypothesis on the nontrivial zeros of the Riemann zeta function $zeta(s)$.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47401634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiplication on Besov and Triebel-Lizorkin spaces of power weights","authors":"Hamza Brahim Boulares, D. Drihem","doi":"10.7169/facm/1991","DOIUrl":"https://doi.org/10.7169/facm/1991","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45707060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mean square value of $L$-functions at $s=1$ for non-primitive characters, Dedekind sumsand bounds on relative class numbers","authors":"S. Louboutin","doi":"10.7169/facm/2027","DOIUrl":"https://doi.org/10.7169/facm/2027","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47935309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the mean square average of Dirichlet $L$-function over characters of odd parityin a special case","authors":"N. E. Thomas, A. Chandran, K. V. Namboothiri","doi":"10.7169/facm/2020","DOIUrl":"https://doi.org/10.7169/facm/2020","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43628873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A characterization of two-weighted inequalities for maximal, singular operators andtheir commutators in generalized weighted Morrey spaces","authors":"C. Aykol, J. Hasanov, Z. Safarov","doi":"10.7169/facm/1924","DOIUrl":"https://doi.org/10.7169/facm/1924","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41988425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the exponential Diophantine equation $F_{n}^{x}+F_{n+1}^{x}+cdots+F_{n+k-1}^{x}=F_{m}$","authors":"F. Luca, E. Tchammou, A. Togbé","doi":"10.7169/facm/1860","DOIUrl":"https://doi.org/10.7169/facm/1860","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46631968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Almost all Fourier coefficients of symmetric power $L$-functions are small","authors":"Henry H. Kim","doi":"10.7169/facm/2082","DOIUrl":"https://doi.org/10.7169/facm/2082","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43396327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Average behaviour of higher moments of cusp form coefficients","authors":"Guodong Hua","doi":"10.7169/facm/1988","DOIUrl":"https://doi.org/10.7169/facm/1988","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47964956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.
在本文中，我们获得了涉及半积分权尖点形式的傅立叶系数的移位卷积和的某些估计。
{"title":"Estimates for the shifted convolution sum involving Fourier coefficients of cusp forms of half-integral weight","authors":"Abash Kumar Jha, L. Vaishya","doi":"10.7169/facm/1942","DOIUrl":"https://doi.org/10.7169/facm/1942","url":null,"abstract":". In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46942195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"One class of continuous functionswith complicated local properties relatednewline to Engel series","authors":"O. Baranovskyi, M. Pratsiovytyi","doi":"10.7169/facm/1963","DOIUrl":"https://doi.org/10.7169/facm/1963","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48939373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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