• Corpus ID: 115177808

Congruences modulo powers of 5 for three-colored Frobenius partitions

  title={Congruences modulo powers of 5 for three-colored Frobenius partitions},
  author={X. Xiong},
  journal={arXiv: Number Theory},
  • X. 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
Congruences for generalized Frobenius partitions with 4 colors
We present some congruences involving the functions [email protected]"4(n) and [email protected]@?"4(n) which denote, respectively, the number of generalized Frobenius partitions of n with 4 colors
An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions
In his 1984 AMS Memoir, George Andrews defined the family of $k$--colored generalized Frobenius partition functions. These are denoted by $c\phi_k(n)$ where $k\geq 1$ is the number of colors in
Infinitely many congruences modulo 5 for 4-colored Frobenius partitions
In his 1984 AMS Memoir, Andrews introduced the family of functions $$c\phi _k(n),$$cϕk(n), which denotes the number of generalized Frobenius partitions of $$n$$n into $$k$$k colors. Recently, Baruah
Congruences for Generalized Frobenius Partitions with an Arbitrarily Large Number of Colors
Several infinite families of congruences for $c\phi_k(n)$ where $k$ is allowed to grow arbitrarily large are proved, relying on a generating function representation which appears in Andrews' Memoir but has gone relatively unnoticed.
Congruence properties for a certain kind of partition functions
In light of the modular equations of fifth and seventh order, we derive some congruence properties for a certain kind of partition functions a(n) which satisfy ∑n=0∞a(n)qn≡(q;q)∞k(modm), where k is a
Generalized Frobenius partitions with 6 colors
We present the generating function for $$c\phi _6(n)$$cϕ6(n), the number of generalized Frobenius partitions of $$n$$n with $$6$$6 colors, in terms of Ramanujan’s theta functions and exhibit $$2$$2,


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.
New congruences for generalized Frobenius partitions with two or three colors
New congruences involving 2-colored and 3-colored generalized Frobenius partitions of n which extend the work of George Andrews and Louis Kolitsch are proved.
A Congruence for Generalized Frobenius Partitions with 3 Colors Modulo Powers of 3
In 1919 Ramanujan conjectured congruences for certain classes of ordi­nary partitions modulo powers of 5 and 7 which were later proved by G.N. Watson. The corresponding congruences for colored
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
A relationship between certain colored generalized Frobenius partitions and ordinary partitions
Ramanujan's congruence p(5n + 4) ≡ 0 (mod 5) for ordinary partitions is well-known. This congruence is just the first in a family of congruences modulo 5; namely, p(5nn + δα) ≡ 0 (mod 5α) for α ≧ 1
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,
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}
Introduction to Elliptic Curves and Modular Forms
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book
Courbes modulaires de genre 1
© Mémoires de la S. M. F., 1975, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// smf.emath.fr/Publications/Memoires/Presentation.html) implique l’accord