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Arithmetic
properties of Schur-type overpartitions
Isaac A. Broudy and Jeremy Lovejoy
Vol. 15 (2022), No. 3, 489–505
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Abstract |
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We investigate arithmetic properties of an overpartition counting function that first arose in connection with Schur’s partition theorem and a universal mock theta function. Motivated by work of Basil Gordon on the Rogers–Ramanujan identities, we first give a complete characterization of the parity of this overpartition function in the progressions , , and in terms of the factorization of for certain and . We then find similar characterizations of the residue modulo in the progressions and . Finally, we prove some Ramanujan-type congruences modulo . Our proofs use basic facts about modular forms and some elementary algebraic number theory. |
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Keywords
partitions, overpartitions, parity, eta-quotients, binary
quadratic forms
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Mathematical Subject Classification
Primary: 11P83
Secondary: 11E25, 11P84
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Milestones
Received: 2 August 2021
Revised: 16 November 2021
Accepted: 18 November 2021
Published: 2 December 2022
Communicated by Ken Ono
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Authors |
| Isaac A. Broudy | |
| Department of Mathematics University of California Berkeley, CA United States |
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| Jeremy Lovejoy | |
| CNRS Université de Paris Paris France |
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