HECKE-TYPE CONGRUENCES FOR ANDREWS' SPT-FUNCTION MODULO 16 AND 32
نویسندگان
چکیده
منابع مشابه
Congruences for Andrews' spt-Function Modulo 32760 and Extension of Atkin's Hecke-Type Partition Congruences
New congruences are found for Andrews’ smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part α(24z) of a certain weak Maass form M(z) of weight 3 2 . We show that a normalized form of the generating function for spt(n) is an eigenform modulo 72 for the Hecke operators T (`2) for primes ` > 3, and an eigenform modulo p for p = 5, 7 or 13 ...
متن کاملCongruences for Andrews’ Spt-function
Congruences are found modulo powers of 5, 7 and 13 for Andrews’ smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan’s partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo ` for all primes ` ≥ 5 which were conjectured earlier by the author. We extend Ono’s method to handle the powers of...
متن کاملCongruences for the Andrews spt function.
Ramanujan-type congruences for the Andrews spt(n) partition function have been found for prime moduli 5 ≤ ℓ ≤ 37 in the work of Andrews [Andrews GE, (2008) J Reine Angew Math 624:133-142] and Garvan [Garvan F, (2010) Int J Number Theory 6:1-29]. We exhibit unexpectedly simple congruences for all ℓ≥5. Confirming a conjecture of Garvan, we show that if ℓ≥5 is prime and (-δ/ℓ) = 1, then spt[(ℓ2(ℓn...
متن کاملCongruences for Andrews ’ Spt - Function modulo Powers of 5 , 7 and 13
Abstract. Congruences are found modulo powers of 5, 7 and 13 for Andrews’ smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan’s partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo for all primes ≥ 5 which were conjectured earlier by the author. We extend Ono’s method to handle the pow...
متن کاملThe spt-function of Andrews.
Recently, Andrews introduced the function s(n) = spt(n) which counts the number of smallest parts among the integer partitions of n. We show that its generating function satisfies an identity analogous to Ramanujan's mock theta identities. As a consequence, we are able to completely determine the parity of s(n). Using another type of identity, one based on Hecke operators, we obtain a complete ...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2014
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042113500991