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On monogenity of certain number fields defined by trinomials 关于三元数定义的某些数域的单胚性
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-09-17 DOI: 10.7169/facm/1987
H. B. Yakkou, L. E. Fadil
{"title":"On monogenity of certain number fields defined by trinomials","authors":"H. B. Yakkou, L. E. Fadil","doi":"10.7169/facm/1987","DOIUrl":"https://doi.org/10.7169/facm/1987","url":null,"abstract":"Let K = Q(θ) be a number field generated by a complex root θ of a monic irreducible trinomial F (x) = x + ax + b ∈ Z[x]. There is an extensive literature of monogenity of number fields defined by trinomials, Gaál studied the multi-monogenity of sextic number fields defined by trinomials. Jhorar and Khanduja studied the integral closedness of Z[θ]. But if Z[θ] is not integrally closed, then Jhorar and Khanduja’s results cannot answer on the monogenity of K. In this paper, based on Newton polygon techniques, we deal with the problem of monogenity of K. More precisely, when ZK 6= Z[θ], we give sufficient conditions on n, a and b for K to be not monogenic. For n ∈ {5, 6, 3, 2 · 3, 2 · 3 + 1}, we give explicitly some infinite families of these number fields that are not monogenic. Finally, we illustrate our results by some computational examples.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49452001","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}
引用次数: 8
Rankin--Cohen brackets on Hermitian Jacobi forms and the adjoint of some linear maps Hermitian Jacobi形式上的Rankin-Cohen括号和一些线性映射的伴随
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-09-13 DOI: 10.7169/facm/1890
S. Sumukha, Singh Sujeet Kumar
{"title":"Rankin--Cohen brackets on Hermitian Jacobi forms and the adjoint of some linear maps","authors":"S. Sumukha, Singh Sujeet Kumar","doi":"10.7169/facm/1890","DOIUrl":"https://doi.org/10.7169/facm/1890","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43488492","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}
引用次数: 0
Accurate computations of Euler products over primes in arithmetic progressions 等差数列中质数上欧拉积的精确计算
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-09-13 DOI: 10.7169/facm/1853
Ramaré Olivier
{"title":"Accurate computations of Euler products over primes in arithmetic progressions","authors":"Ramaré Olivier","doi":"10.7169/facm/1853","DOIUrl":"https://doi.org/10.7169/facm/1853","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44200830","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}
引用次数: 0
On the number of divisors of the least common multiples of shifted prime powers 移质数幂的最小公倍数的除数
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-06-01 DOI: 10.7169/FACM/1866
F. Luca, F. Pappalardi
{"title":"On the number of divisors of the least common multiples of shifted prime powers","authors":"F. Luca, F. Pappalardi","doi":"10.7169/FACM/1866","DOIUrl":"https://doi.org/10.7169/FACM/1866","url":null,"abstract":"In this paper, we give the order of magnitude for the summatory function of the number of divisors of the least common multiple of $p^i-1$ for $i=1,2,ldots,k$ when $ple x$ is prime.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48784409","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}
引用次数: 0
Abstract intersection theory for zeta-functions: geometric aspects zeta函数的抽象交理论：几何方面
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-06-01 DOI: 10.7169/FACM/1916
Grzegorz Banaszak, Y. Uetake
{"title":"Abstract intersection theory for zeta-functions: geometric aspects","authors":"Grzegorz Banaszak, Y. Uetake","doi":"10.7169/FACM/1916","DOIUrl":"https://doi.org/10.7169/FACM/1916","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48980004","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}
引用次数: 0
The construction of the Hilbert genus fields of real cyclic quartic fields 实数循环四次域的Hilbert属域的构造
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-05-24 DOI: 10.7169/facm/2014
M. M. Chems-Eddin, Moulay Ahmed Hajjami, M. Taous
{"title":"The construction of the Hilbert genus fields of real cyclic quartic fields","authors":"M. M. Chems-Eddin, Moulay Ahmed Hajjami, M. Taous","doi":"10.7169/facm/2014","DOIUrl":"https://doi.org/10.7169/facm/2014","url":null,"abstract":"Let k be a number field and let H(k) denote the Hilbert class field of k, that is the maximal abelian unramified extension of k. It is known by class field theory that the Galois group of the extension H(k)/k, i.e., G := Gal(H(k)/k), is isomorphic to Cl(k), the class group of k (cf. [13, p. 228]). The Hilbert genus field of k, denoted by E(k), is the invariant field of G. Thus, by Galois theory, we have: Cl(k)/Cl(k) ≃ G/G ≃ Gal(E(k)/k),","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44343428","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}
引用次数: 0
On sign changes of primitive Fourier coefficients of Siegel cusp forms 关于Siegel尖点形式的原始傅立叶系数的符号变化
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-03-25 DOI: 10.7169/facm/2101
K. D. Shankhadhar, P. Tiwari
{"title":"On sign changes of primitive Fourier coefficients of Siegel cusp forms","authors":"K. D. Shankhadhar, P. Tiwari","doi":"10.7169/facm/2101","DOIUrl":"https://doi.org/10.7169/facm/2101","url":null,"abstract":"In this article, we establish quantitative results for sign changes in certain subsequences of primitive Fourier coefficients of a non-zero Siegel cusp form of arbitrary degree over congruence subgroups. As a corollary of our result for degree two Siegel cusp forms, we get sign changes of its diagonal Fourier coefficients. In the course of our proofs, we prove the non-vanishing of certain type of Fourier-Jacobi coefficients of a Siegel cusp form and all theta components of certain Jacobi cusp forms of arbitrary degree over congruence subgroups, which are also of independent interest.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43693186","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}
引用次数: 1
Euler sums of generalized hyperharmonic numbers 广义超调和数的Euler和
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-03-19 DOI: 10.7169/facm/1953
Rusen Li
{"title":"Euler sums of generalized hyperharmonic numbers","authors":"Rusen Li","doi":"10.7169/facm/1953","DOIUrl":"https://doi.org/10.7169/facm/1953","url":null,"abstract":"are the generalized hyperharmonic numbers (see [4, 10]). Furthermore, H (p,1) n = H (p) n = ∑n j=1 1/n p are the generalized harmonic numbers and H (1,r) n = h (r) n are the classical hyperharmonic numbers. In particularH (1,1) n = Hn are the classical harmonic numbers. Many researchers have been studying Euler sums of harmonic and hyperharmonic numbers (see [4, 6, 7, 9] and references therein), since they play","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47163246","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}
引用次数: 3
Small prime solutions of a Diophantine equation with one prime and five cubes of primes 具有一个素数和五个素数立方的丢芬图方程的小素数解
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-03-01 DOI: 10.7169/FACM/1874
Weiping Li
{"title":"Small prime solutions of a Diophantine equation with one prime and five cubes of primes","authors":"Weiping Li","doi":"10.7169/FACM/1874","DOIUrl":"https://doi.org/10.7169/FACM/1874","url":null,"abstract":"Let $a_1,cdots,a_6$ be non-zero integers satisfying $(a_i,a_j)=1, 1leq i lt j leq 6$ and $b$ be any integer. For the Diophantine equation $a_1p_1+a_2p_2^3+cdots+a_6p_6^3=b$ we prove that (i) if all $a_1,cdots,a_6$ are positive and $bgg max {|a_j|}^{34+varepsilon}$, then the equation is soluble in primes $p_j$, and (ii) if $a_1,cdots,a_6$ are not all of the same sign, then the equation has prime solutions satisfying $max { p_1,p_2^3,cdots,p_6^3 }ll |b|+max {|a_j|}^{33+varepsilon}$, where the implied constants depend only on $varepsilon$.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45672076","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}
引用次数: 0
Elliptic curves with a point of order $13$ defined over cyclic cubic fields 循环三次域上定义的阶点为$13$的椭圆曲线
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-14 DOI: 10.7169/facm/1945
Peter Bruin, M. Derickx, M. Stoll
{"title":"Elliptic curves with a point of order $13$ defined over cyclic cubic fields","authors":"Peter Bruin, M. Derickx, M. Stoll","doi":"10.7169/facm/1945","DOIUrl":"https://doi.org/10.7169/facm/1945","url":null,"abstract":"We show that there is essentially a unique elliptic curve E defined over a cubic Galois extension K of Q with a K-rational point of order 13 and such that E is not defined over Q.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44333860","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}
引用次数: 0
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