The rank of a unimodal sequence and a partial theta identity of Ramanujan

Byungchan Kim; Jeremy Lovejoy

doi:10.1142/S179304211450016X

The rank of a unimodal sequence and a partial theta identity of Ramanujan

Byungchan Kim, Jeremy Lovejoy

School of Natural Sciences

CNRS

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We study the number of unimodal sequences of weight n and rank m using a partial theta identity discovered by Ramanujan. We obtain rank difference identities as well as a congruence for the second rank moment.

Original language	English
Pages (from-to)	1081-1098
Number of pages	18
Journal	International Journal of Number Theory
Volume	10
Issue number	4
DOIs	https://doi.org/10.1142/S179304211450016X
State	Published - Jun 2014

Keywords

Partial theta functions
Rank
Unimodal sequences

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10.1142/S179304211450016X

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abstract = "We study the number of unimodal sequences of weight n and rank m using a partial theta identity discovered by Ramanujan. We obtain rank difference identities as well as a congruence for the second rank moment.",

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AB - We study the number of unimodal sequences of weight n and rank m using a partial theta identity discovered by Ramanujan. We obtain rank difference identities as well as a congruence for the second rank moment.

KW - Partial theta functions

KW - Rank

KW - Unimodal sequences

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DO - 10.1142/S179304211450016X

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JO - International Journal of Number Theory

JF - International Journal of Number Theory

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The rank of a unimodal sequence and a partial theta identity of Ramanujan

Abstract

Keywords

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