Christian Krattenthaler,Wadim Zudilin
Christian Krattenthaler
We give a closed form for quotients of truncated basic hypergeometric series where the base q is evaluated at roots of unity. K...
On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions [0.03%]
Selberg积分的Dotsenko-Fateev复本及扩展
Yury A Neretin
Yury A Neretin
The Selberg integral has a twin ('the Dotsenko-Fateev integral') of the following form. We replace real variables x k in the integrand ∏ | x k | σ - 1 | 1 - x k | τ - 1 ∏ | x k - x l | 2 θ of the Selberg i...
Lukas Mauth
Lukas Mauth
We obtain an exact formula for the cubic partition function and prove a conjecture by Banerjee, Paule, Radu and Zeng. Keywords:...
Cycle integrals of meromorphic modular forms and Siegel theta functions [0.03%]
meromorphic模形式的周期积分与Siegeltheta函数
Markus Schwagenscheidt
Markus Schwagenscheidt
We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the modular curve. We show that suitable linear combinations of these meromorphic modular forms ...
A single-variable proof of the omega SPT congruence family over powers of 5 [0.03%]
关于五的幂的Omega-SPT同余族的单变量证明
Nicolas Allen Smoot
Nicolas Allen Smoot
In 2018, Liuquan Wang and Yifan Yang proved the existence of an infinite family of congruences for the smallest parts function corresponding to the third-order mock theta function ω(q). Their proof took the form of an induction requiri...
Koustav Banerjee,Peter Paule,Cristian-Silviu Radu et al.
Koustav Banerjee et al.
Let p(n) denote the number of partitions of n. A new infinite family of inequalities for p(n) is presented. This generalizes a result by William Chen et al. From this infinite family, another infinite family of inequalities for logp(n) is d...
Michael J Schlosser,Nian Hong Zhou
Michael J Schlosser
In this paper, we study properties of the coefficients appearing in the q-series expansion of ∏n≥1[(1-qn)/(1-qpn)]δ, the infinite Borwein product for an arbitrary prime p, raised to an arbitrary positive real power δ. ...
George E Andrews,Ali K Uncu
George E Andrews
This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends. ...
Gargi Mukherjee
Gargi Mukherjee
Let p ¯ ( n ) denote the overpartition function. In this paper, we obtain an inequality for the sequence Δ 2 log p ¯ ( n - 1 ) / ( n - 1 ) α n - 1 which states that log ( 1 + 3 π 4 n 5 / 2 - 11 + 5 &...
On sums of coefficients of polynomials related to the Borwein conjectures [0.03%]
与Borwein猜想有关的多项式系数和的研究
Ankush Goswami,Venkata Raghu Tej Pantangi
Ankush Goswami
Recently, Li (Int J Number Theory, 2020) obtained an asymptotic formula for a certain partial sum involving coefficients for the polynomial in the First Borwein conjecture. As a consequence, he showed the positivity of this sum. His result ...