共查询到20条相似文献,搜索用时 15 毫秒
1.
The Ramanujan Journal - Assuming the Riemann hypothesis, we prove that $$\begin{aligned} N_k(T) = \frac{T}{2\pi }\log \frac{T}{4\pi e} + O_k\bigg (\frac{\log T}{\log \log T}\bigg ), \end{aligned}$$... 相似文献
2.
The Ramanujan Journal - Let $$k\geqslant 2$$ be a fixed natural number and $$d_k(n)$$ denote the number of ways n can be written as a product of k positive integers. We use $$\Delta _k(x)$$ to... 相似文献
3.
The Ramanujan Journal - Recently, Andrews, Dixit, and Yee defined two partition functions $$p_{\omega }(n)$$ and $$p_{\nu }(n)$$ that are related with Ramanujan’s mock theta functions... 相似文献
4.
Amrik Singh Nimbran 《印度理论与应用数学杂志》2016,47(4):697-703
In this note we present some sundry infinite products for \(\sqrt 2 \) and six general formulas for some rational powers of 2. 相似文献
5.
The Ramanujan Journal - The two partition functions $$p_\omega (n)$$ and $$p_\nu (n)$$ were introduced by Andrews, Dixit and Yee, which are related to the third-order mock theta functions $$\omega... 相似文献
6.
In this paper, we are concerned with general fractional differential equations of order \(\alpha \in (1,2)\) and type \(\beta \in [0,1]\) in Banach spaces. We define and develop a theory of general fractional sine functions and show that they are essentiality equivalent to a general fractional resolvent. We use such theory to study the well-posedness of the above general fractional differential equations. An illustration example is presented. 相似文献
7.
George E. Andrews Donny Passary James A. Sellers Ae Ja Yee 《The Ramanujan Journal》2017,42(2):347-361
We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type \(_2F_{1}\). Consequently, we obtain some new expressions for the celebrated Fibonacci numbers and their derivative sequences. Moreover, we evaluate some definite integrals involving products of Fibonacci and Chebyshev polynomials. 相似文献
8.
The Ramanujan Journal - In this note, using the well-known series representation for the Clausen function, we also provide some new representations of Apery’s constant $$\zeta (3)$$ . In... 相似文献
9.
Journal of Algebraic Combinatorics - We show that the $$\gamma $$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In... 相似文献
10.
In this paper, we provide a new proof for the Dedekind \(\eta \)-function identities discovered by Somos. During this process, we found two new Dedekind \(\eta \)-function identities. Furthermore, we extract interesting partition identities from some of the \(\eta \)-function identities. 相似文献
11.
The Ramanujan Journal - By examining known q-series identities, we derive q-analogues of several $$\pi $$ -related infinite series, including some of Ramanujan’s series for $$1/\pi $$ . 相似文献
12.
The Ramanujan Journal - We are concerned with counting self-conjugate $$(s,s+1,s+2)$$ -core partitions. A Motzkin path of length n is a path from (0, 0) to (n, 0) which stays... 相似文献
13.
Annali di Matematica Pura ed Applicata (1923 -) - In a recent work on Euler-type formulae for even Dirichlet beta values, i.e., $$\beta {(2n)}$$ , I have derived an exact closed-form expression for... 相似文献
14.
A combinatorial proof that the number of points of the space \(\overline {{M_{0,n}}} \left( {{F_q}} \right)\) satisfies the recurrent formula for the Poincaré polynomials of the space \(\overline {{M_{0,n}}} \left( \mathbb{C} \right)\) is obtained. 相似文献
15.
Archiv der Mathematik - We study the validity of the distributivity equation $$\begin{aligned} ({\mathcal {A}}\otimes {\mathcal {F}})\cap ({\mathcal {A}}\otimes {\mathcal {G}}) ={\mathcal... 相似文献
16.
The Ramanujan Journal - Recently Gordon and McIntosh introduced the third order mock theta function $$\xi (q)$$ defined by $$\begin{aligned} \xi (q)=1+2\sum _{n=1}^{\infty... 相似文献
17.
Positivity - We prove that the category of Dedekind $$\sigma $$ -complete Riesz spaces is an infinitary variety, and we provide an explicit equational axiomatization. In fact, we show that finitely... 相似文献
18.
Lei Yang 《The Ramanujan Journal》2017,42(3):689-712
We give an explicit formula for the Hauptmodul \(\left( \frac{\eta (\tau )}{\eta (13 \tau )}\right) ^2\) of the level-13 Hecke modular group \(\Gamma _0(13)\) as a quotient of theta constants, together with some related explicit formulas. Similar results for primes \(p=2, 3, 5, 7\) (the other p for which \(\Gamma _0(p)\) has genus zero) are well known, and date back to Klein and Ramanujan. Moreover, we find an exotic modular equation, i.e., it has the same form as Ramanujan’s modular equation of degree 13, but with different kinds of modular parameterizations. 相似文献
19.
Xuejun Zhang Yuting Guo Qingli Shang Shenlian Li 《Complex Analysis and Operator Theory》2018,12(5):1251-1265
In this paper, the authors prove that the Gleason’s problem is solvable on the logarithm weight general function spaces F(p,q,s,k) in the unit ball \(B\subset \mathbf{C^{n}}\). 相似文献
20.
We find several new congruences for \(\ell \)-regular partitions for \(\ell \in \{5,6,7,49\}\) and also find alternative proofs of the congruences for 10- and 20-regular partitions which were proved earlier by Carlson and Webb (Ramanujan J 33:329–337, 2014) by using the theory of modular forms. We use certain p-dissections of \((q;q)_{\infty }\), \(\psi (q)\), \((q;q)_{\infty }^3\) and \(\psi (q^2)(q;q)_{\infty }^2\). 相似文献