Factors of Some Lacunary q-Binomial Sums

Details Factors of Some Lacunary q-Binomial Sums Factors of Some Lacunary q-Binomial Sums

2012-01-28

arxiv.org/abs/1201.5963v2

Mathematics

Number Theory

Scientific paper

In this paper, we prove a divisibility result for the lacunary $q$-binomial
sum $$ \sum_{k\equiv
r\pmod{c}}(-1)^kq^{\binom{k}{2}}\qbinom{n}{k}{q}\qbinom{(k-r)/c}{l}{q^{c}}. $$

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