RELATION BETWEEN A MOCK MODULAR FORM AND ITS SHADOW THROUGH LIMIT VALUES

Dohoon Choi; Subong Lim

doi:10.1090/proc/17164

RELATION BETWEEN A MOCK MODULAR FORM AND ITS SHADOW THROUGH LIMIT VALUES

Dohoon Choi
, Subong Lim

Department of Mathematics

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

Abstract

In his last letter to Hardy, Ramanujan defined 17 mock theta functions, and Zwegers discovered that they are holomorphic parts of harmonic weak Maass forms of weight ¹₂ . Zagier defined a mock modular form as the holomorphic part of a harmonic weak Maass form F. The nonholomorphic part of F can be obtained by the nonholomorphic Eichler integral of a cusp form, which is called the shadow. In this paper, we study the relation between a mock modular form and its shadow through limit values of a mock modular form when a mock modular form has weight k ∈ ¹₂ Z such that k ≤ −2.

Original language	English
Pages (from-to)	2407-2417
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	153
Issue number	6
DOIs	https://doi.org/10.1090/proc/17164
Publication status	Published - 2025 Jun

Bibliographical note

Publisher Copyright:
© 2025 American Mathematical Society.

Keywords

Mock modular form
limit values
shadow

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/17164

Cite this

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abstract = "In his last letter to Hardy, Ramanujan defined 17 mock theta functions, and Zwegers discovered that they are holomorphic parts of harmonic weak Maass forms of weight 12 . Zagier defined a mock modular form as the holomorphic part of a harmonic weak Maass form F. The nonholomorphic part of F can be obtained by the nonholomorphic Eichler integral of a cusp form, which is called the shadow. In this paper, we study the relation between a mock modular form and its shadow through limit values of a mock modular form when a mock modular form has weight k ∈ 12 Z such that k ≤ −2.",

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ER -

RELATION BETWEEN A MOCK MODULAR FORM AND ITS SHADOW THROUGH LIMIT VALUES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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