Ramanujan Journal
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0.84
Papers
1,825
Papers 1,707
1 page of 171 pages (1,707 results)
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#1Lenny Jones (SU: Shippensburg University)H-Index: 7
Let $D_n denote the dihedral group of order 2n. We find infinite D_6 -families and an infinite D_3 -family of monic irreducible reciprocal sixth-degree polynomials f(x)\in \mathbb {Z}[x] , such that \{1,\theta ,\theta ^2,\theta ^3,\theta ^4,\theta ^5\} is a basis for the ring of integers of L=\mathbb {Q}(\theta ) , where f(\theta )=0 .
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#1Lulu Fang (NUST: Nanjing University of Science and Technology)H-Index: 4
#2Jihua Ma (WHU: Wuhan University)H-Index: 2
Last. Kunkun Song (WHU: Wuhan University)H-Index: 4
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Let $[a_1(x),a_2(x), a_3(x),\ldots ] denote the continued fraction expansion of a real number x \in [0,1) . This paper is concerned with certain exceptional sets of the Borel–Bernstein Theorem on the growth rate of \{a_n(x)\}_{n\geqslant 1} . As a main result, the Hausdorff dimension of the set \begin{aligned} E_{\sup }(\psi )=\left\{ x\in [0,1):\ \limsup \limits _{n\rightarrow \infty }\frac{\log a_n(x)}{\psi (n)}=1\right\} \end{aligned} is determined, where \psi :{\mathbb {N}}\...
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#1David Klein (TU Darmstadt)H-Index: 1
#2Jennifer Kupka (TU Darmstadt)H-Index: 1
We present completions of mock theta functions to harmonic weak Maass forms of weight $\nicefrac {1}{2} and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight \nicefrac {1}{2} that have mock theta functions as their holomorphic part. Using these harmonic weak Maass forms and the Millson theta lift, we compute finite algebraic formulas for the coefficients of the appearing mock theta functions in terms of traces of singular ...
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#1Kui Liu (Qingdao University)H-Index: 1
#2Xianchang Meng (GAU: University of Göttingen)H-Index: 3
This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze more carefully about both the “visible” points and the “invisible” points in the definition of previous research. We prove asymptotic formulas for the number of lattice points in different levels of visibility.
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#1Mircea Merca (University of Craiova)H-Index: 1
In this paper we show that the reciprocal of the finite product $(q;q)_n can be expressed as a sum over all the partitions of n in two different ways. We derive similar results for the reciprocal of 1-q^n . Product identities involving sums over partitions are derived as consequences of these results.
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#1Paul Terwilliger (UW: University of Wisconsin–Madison)H-Index: 34
The q-Onsager algebra null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null ${\mathcal {O}}_q null null null null null null null null null null null null null null null null null null null null null null null null null null is defined by two generators A, null ...
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#1Jinjiang Li (CUMT: China University of Mining and Technology)H-Index: 2
#2Min Zhang (BISTU: Beijing Information Science & Technology University)H-Index: 2
Last. Fei Xue (CUMT: China University of Mining and Technology)H-Index: 2
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Let N be a sufficiently large real number. In this paper, it is proved that, for null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null $1
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#1Mircea Merca (University of Craiova)H-Index: 1
The partitions in which even parts come in two colours are known as cubic partitions. In this paper, we introduce and investigate the cubic partition function A(n) which is defined as the difference between the number of cubic partitions of n into an even numbers of parts and the number of cubic partitions of n into an odd numbers of parts. We present a collection of identities relating A(n) and provide analytic proofs. Among these identities we remark two Ramanujan-like congruences: for all nul...
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#1D. Yu. Melikdzhanian (TSU: Tbilisi State University)
#2Artur Ishkhanyan (RAU: Russian-Armenian University)H-Index: 23
Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination of two confluent generalized hypergeometric functions are identified. The involved hypergeometric functions, which in general do not reduce to polynomials, are such that each numerator parameter (except one) exceeds a corresponding denominator parameter by unity.
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