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Ramanujan-type congruences for partition k-tuples with 5-cores

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Abstract

We prove several Ramanujan-type congruences modulo powers of 5 for partition k-tuples with 5-cores, for \(k=2, 3, 4\). We also prove some new infinite families of congruences modulo powers of primes for k-tuples with p-cores, where p is a prime.

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References

  1. Bruce C. Berndt. Ramanujan’s notebooks. Part III. Springer-Verlag, New York, 1991.

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  2. Bruce C. Berndt. Number theory in the spirit of Ramanujan, volume 34 of Student Mathematical Library. American Mathematical Society, Providence, RI, 2006.

  3. N. V. Majid and S. N. Fathima. On a Ramanujan-type congruence for partition triples with 5-cores. J. Integer Seq., 25(6):Art. 22.6.2, 7, 2022.

  4. Dasappa Ranganatha. On a Ramanujan-type congruence for bipartitions with 5-cores. J. Integer Seq., 19(8):Art. 16.8.1, 5, 2016.

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Acknowledgements

The authors are thankful to the anonymous referee for his/her helpful comments on the paper. The authors would like to thank Prof. Nayandeep Deka Baruah for his encouragement and support. The second author was partially supported by an institutional fellowship for doctoral research from Tezpur University, Napaam, India. The third author was partially supported by the Council of Scientific & Industrial Research (CSIR), Government of India under the CSIR-JRF scheme. (Grant No 09/0796(12991)/2021-EMRI). The authors thank their respective funding agencies.

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Authors and Affiliations

  1. Mathematical and Physical Sciences Division, School of Arts and Sciences, Ahmedabad University, Navrangpua, Ahmedabad, Gujarat, 380009, India

    Manjil P. Saikia

  2. Department of Mathematical Sciences, Tezpur University, Napaam, Assam, 784028, India

    Abhishek Sarma & Pranjal Talukdar

Authors
  1. Manjil P. Saikia
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  2. Abhishek Sarma
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  3. Pranjal Talukdar
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Correspondence to Pranjal Talukdar.

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Communicated by B. Sury.

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Saikia, M.P., Sarma, A. & Talukdar, P. Ramanujan-type congruences for partition k-tuples with 5-cores. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00566-8

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  • DOI: https://doi.org/10.1007/s13226-024-00566-8

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