Completions and algebraic formulas for the coefficients of Ramanujan's mock theta functions [0.03%]
Ramanujan拟theta函数系数的完备代数公式
David Klein,Jennifer Kupka
David Klein
We present completions of mock theta functions to harmonic weak Maass forms of weight 1 2 and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight 1 2 that have mock thet...
Highly composite polynomials and the maximum order of the divisor function in [Formula: see text] [0.03%]
高合成多项式及除数函数在[公式：见文本]中的最大阶数
Ardavan Afshar
Ardavan Afshar
We investigate the analogues, in F q [ t ] , of highly composite numbers and the maximum order of the divisor function, as studied by Ramanujan. In particular, we determine a family of highly composite polynomials which is not too sparse...
On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences [0.03%]
关于Lucas序列连续两项幂的指数Diophantine方程
Mahadi Ddamulira,Florian Luca
Mahadi Ddamulira
Let r ≥ 1 be an integer and U : = ( U n ) n ≥ 0 be the Lucas sequence given by U 0 = 0 , U 1 = 1 , and U n + 2 = r U n + 1 + U n , for all n ≥ 0 . In this paper, we show that there are no positive integers r ...
Shōta Inoue,Sumaia Saad Eddin,Ade Irma Suriajaya
Shōta Inoue
Let f be an arithmetic function and let S # denote the extended Selberg class. We denote by L ( s ) = ∑ n = 1 ∞ f ( n ) n s the Dirichlet series attached to f. The Laurent-Stieltjes constants of L ( s ) , which belongs to ...
An application of hypergeometric functions to heat kernels on rectangular and hexagonal tori and a "Weltkonstante"-or-how Ramanujan split temperatures [0.03%]
Heck函数在矩形和六角形环上的Heat核中的应用及“世界常数”-或-Ramanujan如何划分温度上限
Markus Faulhuber
Markus Faulhuber
In this work we investigate the heat kernel of the Laplace-Beltrami operator on a rectangular torus and the according temperature distribution. We compute the minimum and the maximum of the temperature on rectangular tori of fixed area by m...
Uniform convergence of basic Fourier-Bessel series on a q-linear grid [0.03%]
q-线性格上基本傅里叶-贝塞尔级数的一致收敛性
L D Abreu,R Álvarez-Nodarse,J L Cardoso
L D Abreu
We study Fourier-Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The convergence result...
Heine's method and [Formula: see text] to [Formula: see text] transformation formulas [0.03%]
汉纳的求和方法与从[Formula: see text]到[Formula: see text]的变换公式
Gaurav Bhatnagar
Gaurav Bhatnagar
We apply Heine's method-the key idea Heine used in 1846 to derive his famous transformation formula for 2 ϕ 1 series-to multiple basic series over the root system of type A. In the classical case, this leads to a bibasic extension ...
Romanov type problems [0.03%]
罗马诺夫型问题
Christian Elsholtz,Florian Luca,Stefan Planitzer
Christian Elsholtz
Romanov proved that the proportion of positive integers which can be represented as a sum of a prime and a power of 2 is positive. We establish similar results for integers of the form n = p + 2 2 k + m ! and n = p + 2 2 k + 2 q where ...
Andrew Granville,Dimitris Koukoulopoulos
Andrew Granville
The Landau-Selberg-Delange method gives an asymptotic formula for the partial sums of a multiplicative function f whose prime values are α on average. In the literature, the average is usually taken to be α with a very strong erro...