Construction and Application of a Class of Modular Functions (II)†

Newman, Morris

doi:10.1112/plms/s3-9.3.373

Cited by 143 publications

(77 citation statements)

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“…By a well-known theorem of Gordon, Hughes and Newman ([9], [13]) on η-quotients, it is always a modular form of negative weight 1 2 (1 − k) and level 24k (or any level this divides). Together these two facts promise us the existence of many congruences and give us numerous tools in the literature to prove them.…”

Section: (K K − 1)-colored Partitionsmentioning

confidence: 99%

Restricted k-color partitions

Keith

2015

Ramanujan J

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Abstract. We generalize overpartitions to (k, j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems: generating function dissections, modular forms, bijections, and other combinatorial maps. We find connections to divisor sums, the Han/Nekrasov-Okounkov hook length formula and a possible approach to a finitization, and other topics, suggesting that a rich mine of results is available.

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Section: (K K − 1)-colored Partitionsmentioning

confidence: 99%

Restricted k-color partitions

Keith

2015

Ramanujan J

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“…see [22]. Furthermore, it is invariant under the Fricke-Atkin-Lehner involution of level N by [10], Theorem 2, and an element of F N , the field of modular functions of level N whose q-expansions at any cusp lie in the N -th cyclotomic field, by Theorem 7 of [10].…”

Section: Double η Quotients As Class Invariantsmentioning

confidence: 99%

Constructing elliptic curves over finite fields using double eta-quotients

Enge¹,

Schertz²

2004

J. Théor. Nombres Bordeaux

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“…The following result was proved by Morris Newman [11]. It is now straightforward to verify that g 1 (z), g 2 (z), g 3 (z), g 4 (z) are modular functions on Γ 0 (84).…”

mentioning

confidence: 95%