Ramanujan congruences for a class of eta quotients

2008/10/10 by Jonah Sinick, Sinick, Jonah
Mathematics · #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0810.1931

openalex publication_date 2008/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓ n + a) ≡ 0 \pmod ℓ. We apply this result to obtain a complete characterization of the congruences of the same form that the sequences c_N(n) satisfy, where c_N(n) is defined by ∑_n=0^∞ c_N(n)qⁿ = ∏_n=1^∞ \frac1(1-qⁿ)(1-q^Nn). This last result answers a question of H.-C. Chan.

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