Add to ORKGIn 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n) modulo powers of the primes 5,7,11. In this work, we study Ramanujan type congruences modulo powers of primes p = 7,11,13,17,19,23 satisfied by the Fourier coefficients of quotients the Rogers-Ramanujan Functions G(τ) and H(τ) and the Dedekind eta function η(5τ). In addition to deriving new congruences, we develop the foundational theory of modular forms to motivate and prove the results. The work includes proofs of congruences facilitated by Python/SageMath code
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractThe discovery of some partition function congruences by Ramanujan, and subsequent research m...
Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dis...
In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n...
This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms...
MacMahon provided Ramanujan and Hardy a table of values for p(n) with the partitions of the first 20...
In his notebooks, Ramanujan recorded 40 beautiful modular relations for the Rogers-Ramanujan functio...
We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously...
AbstractOn page 189 in his lost notebook, Ramanujan recorded five assertions about partitions. Two a...
Recently, the authors have established a large class of modular relations involving the Rogers-Raman...
Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent Unive...
In this paper, we consider the Rogers-Ramanujan type functions J(q) and K(q) of order ten and establ...
AbstractIn a manuscript of Ramanujan, published with his Lost Notebook [21, pp. 236–237], there are ...
AbstractA famous identity of Ramanujan connected with partitions modulo 5 is shown to be equivalent ...
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful...
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractThe discovery of some partition function congruences by Ramanujan, and subsequent research m...
Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dis...
In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n...
This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms...
MacMahon provided Ramanujan and Hardy a table of values for p(n) with the partitions of the first 20...
In his notebooks, Ramanujan recorded 40 beautiful modular relations for the Rogers-Ramanujan functio...
We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously...
AbstractOn page 189 in his lost notebook, Ramanujan recorded five assertions about partitions. Two a...
Recently, the authors have established a large class of modular relations involving the Rogers-Raman...
Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent Unive...
In this paper, we consider the Rogers-Ramanujan type functions J(q) and K(q) of order ten and establ...
AbstractIn a manuscript of Ramanujan, published with his Lost Notebook [21, pp. 236–237], there are ...
AbstractA famous identity of Ramanujan connected with partitions modulo 5 is shown to be equivalent ...
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful...
AbstractThe three sequences mentioned in the title are Ramanujan's τ-function, the coefficients cn o...
AbstractThe discovery of some partition function congruences by Ramanujan, and subsequent research m...
Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dis...