Kida's formula in classical Iwasawa theory relates the Iwasawa lambda-invariants of p-extensions of number fields. Analogue of this formula was subseq......
Let N be the set of positive integers and k >= 3 be an integer. Define the set G subset of (0, 1] of real numbers as a k-good set if G contains no ......
Quite recently, Xia and Zhao established the 10-dissections for Hirschhorn's two infinite q-series products by using two MAPLE packages and the theory......
In this paper, we represent the generating function of the rank function as a summation of four parts-a constant, two Lambert series and a product. Ap......
In this paper, we study the coefficient estimates for a class of analytic functions defined by using the q-Ruscheweyh derivative operator. In particul......
Andrews introduced odd Durfee symbols to give an interesting combinatorial interpretation of omega(q) invoked by MacMahon's modular partitions, where ......
Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, we generalize the result of Vaughan (Bul......
The Kronecker theta function is a quotient of the Jacobi theta functions, which is also a special case of Ramanujan's (1)psi(1) summation. Using the K......
In this paper, we generalize Elliott's weighted Erdos-Kac theorem to the case of short intervals.
An upper quasi-density onH(the integers or the non-negative integers) is a real-valued subadditive function mu(star) defined on the whole power set of......
Using Andrews' multiseries generalization of Watson's (8)phi(7) transformation, we give a new extension of the (H.2) supercongruence of Van Hamme for ......
In this note, we revisit Ramanujan's function k(tau) and discuss various results, old and new, on it in modular-functional context.
In this paper, we study Ramanujan sums c(J)(I), where I and J are integral ideals in an arbitrary quadratic number field. In particular, the asymptoti......
Let k >= 4 be an integer. Suppose that lambda(1),lambda(2),lambda(3),lambda(4) are positive real numbers, lambda(1)/lambda(2) is irrational and alg......
Recently, Andrews and Merca obtained two identities concerning the number of even parts in all partitions of n into distinct parts. In this paper, we ......
