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On Hermitian Eisenstein series of degree $2$ 关于2次的厄米爱森斯坦级数
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2022-01-01 DOI: 10.7169/facm/2047
Adrian Hauffe-Waschbusch, A. Krieg, Brandon Williams
{"title":"On Hermitian Eisenstein series of degree $2$","authors":"Adrian Hauffe-Waschbusch, A. Krieg, Brandon Williams","doi":"10.7169/facm/2047","DOIUrl":"https://doi.org/10.7169/facm/2047","url":null,"abstract":"We consider the Hermitian Eisenstein series $E^{(mathbb{K})}_k$ of degree $2$ and weight $k$ associated with an imaginary-quadratic number field $mathbb{K}$ and determine the influence of $mathbb{K}$ on the arithmetic and the growth of its Fourier coefficients. We find that they satisfy the identity $E^{{(mathbb{K})}^2}_4 = E^{{(mathbb{K})}}_8$, which is well-known for Siegel modular forms of degree $2$, if and only if $mathbb{K} = mathbb{Q} (sqrt{-3})$. As an application, we show that the Eisenstein series $E^{(mathbb{K})}_k$, $k=4,6,8,10,12$ are algebraically independent whenever $mathbb{K}neq mathbb{Q}(sqrt{-3})$. The difference between the Siegel and the restriction of the Hermitian to the Siegel half-space is a cusp form in the Maass space that does not vanish identically for sufficiently large weight; however, when the weight is fixed, we will see that it tends to $0$ as the discriminant tends to $-infty$. Finally, we show that these forms generate the space of cusp forms in the Maass Spezialschar as a module over the Hecke algebra as $mathbb{K}$ varies over imaginary-quadratic number fields.","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":"43307070","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: 2
Ulam stability of a quadratic-type functional equation in 3 variables in the quasi-Banach space 拟banach空间中3变量二次型泛函方程的Ulam稳定性
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2022-01-01 DOI: 10.7169/facm/1934
Ravi Sharma, S. Chandok
{"title":"Ulam stability of a quadratic-type functional equation in 3 variables in the quasi-Banach space","authors":"Ravi Sharma, S. Chandok","doi":"10.7169/facm/1934","DOIUrl":"https://doi.org/10.7169/facm/1934","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":"48603871","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
An explicit evaluation of $10^{text{th}}$-power moment of quadratic Gauss sums and some applications 二次高斯和$10^{text{th}}$幂矩的显式求值及其应用
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2022-01-01 DOI: 10.7169/facm/1995
Nilanjan Bag, Antonio Rojas-León, Zhang Wenpeng
{"title":"An explicit evaluation of $10^{text{th}}$-power moment of quadratic Gauss sums and some applications","authors":"Nilanjan Bag, Antonio Rojas-León, Zhang Wenpeng","doi":"10.7169/facm/1995","DOIUrl":"https://doi.org/10.7169/facm/1995","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":"46082326","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
Galois realization of Schur covers of dihedral groups of $2$-power order $2$-幂阶二面体群Schur覆盖的Galois实现
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2022-01-01 DOI: 10.7169/facm/1975
Ryosuke Amano, Akira Ishimaru, Masanari Kida
{"title":"Galois realization of Schur covers of dihedral groups of $2$-power order","authors":"Ryosuke Amano, Akira Ishimaru, Masanari Kida","doi":"10.7169/facm/1975","DOIUrl":"https://doi.org/10.7169/facm/1975","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":"48025337","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
Hadamard product of series with special numbers 特殊数级数的阿达玛积
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2022-01-01 DOI: 10.7169/facm/2050
Khristo N. Boyadzhiev, R. Frontczak
{"title":"Hadamard product of series with special numbers","authors":"Khristo N. Boyadzhiev, R. Frontczak","doi":"10.7169/facm/2050","DOIUrl":"https://doi.org/10.7169/facm/2050","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":"47604231","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
The $p$-adic Duffin-Schaeffer conjecture $p$adic-Duffin-Scheeffer猜想
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-10-06 DOI: 10.7169/facm/2042
S. Kristensen, M. Laursen
{"title":"The $p$-adic Duffin-Schaeffer conjecture","authors":"S. Kristensen, M. Laursen","doi":"10.7169/facm/2042","DOIUrl":"https://doi.org/10.7169/facm/2042","url":null,"abstract":". We prove Haynes’ version of the Duffin–Schaeffer conjecture for the p -adic numbers. In addition, we prove several results about an associated related but false conjecture, related to p -adic approximation in the spirit of Jarn´ık and Lutz.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48928543","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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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