The 5-dissections of two infinite product expansions

In this paper, we establish 5-dissections of two infinite products and thereby prove that their q -series coefficients vanish for two arithmetic progressions. Moreover, our results also imply that the signs of coefficients of these infinite products are periodic with period 5 from n > 1 .

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Veröffentlicht in:	The Ramanujan journal 2021-04, Vol.54 (3), p.475-484
Hauptverfasser:	Dou, Donna Q. J., Xiao, Jiejuan
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Dissection Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory Progressions Series (mathematics)
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Beschreibung
Zusammenfassung:	In this paper, we establish 5-dissections of two infinite products and thereby prove that their q -series coefficients vanish for two arithmetic progressions. Moreover, our results also imply that the signs of coefficients of these infinite products are periodic with period 5 from n > 1 .
ISSN:	1382-4090 1572-9303
DOI:	10.1007/s11139-019-00200-w