Universität zu Köln

Bringmann, Kathrin, Ono, Ken and Wagner, Ian . Eichler integrals of Eisenstein series as q-brackets of weighted t-hook functions on partitions. Ramanujan J.. DORDRECHT: SPRINGER. ISSN 1572-9303

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Abstract

We consider the t-hook functions on partitions f(a,t) : P -> C defined by f(a,t)(lambda) : = t(a-1) Sigma(h is an element of Ht(lambda)) 1/ha, where H-t (lambda) is the multiset of partition hook numbers that are multiples of t. The Bloch-Okounkov q-brackets < fa,t > q include Eichler integrals of the classical Eisenstein series. For even a >= 2, we show that these q-brackets are natural pieces of weight 2 - a sesquiharmonic and harmonic Maass forms, while for odd a <= -1, we show that they are holomorphic quantum modular forms. We use these results to obtain new formulas of Chowla-Selberg type, and asymptotic expansions involving values of the Riemann zeta-function and Bernoulli numbers. We make use of work of Berndt, Han and Ji, and Zagier.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bringmann, Kathrin UNSPECIFIED UNSPECIFIED UNSPECIFIED Ono, Ken UNSPECIFIED UNSPECIFIED UNSPECIFIED Wagner, Ian UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-580084
DOI:	10.1007/s11139-021-00453-4
Journal or Publication Title:	Ramanujan J.
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9303
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FORMS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/58008