A Determinantal Congruence Related to Bilinear Forms (mod p...).

John H. Hodges

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Displaying similar documents to “A Determinantal Congruence Related to Bilinear Forms (mod p...).”

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Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3)...