• Corpus ID: 115177808

Congruences modulo powers of 5 for three-colored Frobenius partitions

@article{Xiong2010CongruencesMP,
  title={Congruences modulo powers of 5 for three-colored Frobenius partitions},
  author={Xinhua Xiong},
  journal={arXiv: Number Theory},
  year={2010}
}
  • Xinhua Xiong
  • Published 27 February 2010
  • Mathematics
  • arXiv: Number Theory
Motivated by a question of Lovejoy \cite{lovejoy}, we show that three-colored Frobenius partition function $\c3$ and related arithmetic fuction $\cc3$ vanish modulo some powers of 5 in certain arithmetic progressions. 
6 Citations

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References

SHOWING 1-10 OF 12 REFERENCES

Ramanujan-Type Congruences for Three Colored Frobenius Partitions

Abstract Using the theory of modular forms, we show that the three-colored Frobenius partition function vanishes modulo some small primes in certain arithmetic progressions.

Congruences for Frobenius Partitions

Abstract The partition functionp(n) has several celebrated congruence properties which reflect the action of the Hecke operators on certain holomorphic modular forms. In this article similar

Parity of the Partition Function in Arithmetic Progressions, II

Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N = r (mod t) for which p(N) is even, and

A simple proof of the Ramanujan conjecture for powers of 5.

Ramanujan conjectured, and G. N. Watson proved, that if n is of a specific form then p (n), the number of partitions of «, is divisible by a high power of 5. In the present note, we establish

Congruences for partition functions

The ordinary partition function p(n) and some of its generalizations satisfy some beautiful congruence properties. For instance, Ramanujan proved that for every integer n $$\begin{array}{*{20}c}

Courbes modulaires de genre 1

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Parity of the partition function in arithmetic progressions.