Genius Whom the Gods Loved— A Review of “Srinivasa Ramanujan: The Lost Notebook and Other Unpublished Papers”

2021 ◽  
pp. 131-133
Author(s):  
Krishnaswami Alladi
Keyword(s):  
Lost Notebook

Erratum to: The Lost Notebook of ENRICO FERMI

2018 ◽  
pp. E1-E1
Author(s):  
Francesco Guerra ◽  
Nadia Robotti
Keyword(s):  
Enrico Fermi ◽  
Lost Notebook

The final problem: an identity from Ramanujan's lost notebook

2019 ◽  
Vol 100 (2) ◽  
pp. 568-591 ◽  
Author(s):  
Bruce C. Berndt ◽  
Junxian Li ◽  
Alexandru Zaharescu
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook

scholarly journals A quasi-theta product in Ramanujans lost notebook

2003 ◽  
Vol 135 (1) ◽  
pp. 11-18 ◽  
Author(s):  
BRUCE C. BERNDT ◽  
HENG HUAT CHAN ◽  
ALEXANDRU ZAHARESCU
Keyword(s):  
Lost Notebook

scholarly journals Congruences for sixth order mock theta functions $ \lambda(q) $ and $ \rho(q) $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Harman Kaur ◽  
Meenakshi Rana
Keyword(s):  
Theta Functions ◽  
Sixth Order ◽  
Mock Theta Functions ◽  
Lost Notebook

<p style='text-indent:20px;'>Ramanujan introduced sixth order mock theta functions <inline-formula><tex-math id="M3">\begin{document}$ \lambda(q) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \rho(q) $\end{document}</tex-math></inline-formula> defined as:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} \lambda(q) &amp; = \sum\limits_{n = 0}^{\infty}\frac{(-1)^n q^n (q;q^2)_n}{(-q;q)_n},\\ \rho(q) &amp; = \sum\limits_{n = 0}^{\infty}\frac{ q^{n(n+1)/2} (-q;q)_n}{(q;q^2)_{n+1}}, \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>listed in the Lost Notebook. In this paper, we present some Ramanujan-like congruences and also find their infinite families modulo 12 for the coefficients of mock theta functions mentioned above.</p>

FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS

2018 ◽  
Vol 239 ◽  
pp. 173-204 ◽  
Author(s):  
GEORGE E. ANDREWS ◽  
BRUCE C. BERNDT ◽  
SONG HENG CHAN ◽  
SUN KIM ◽  
AMITA MALIK
Keyword(s):  
Generating Functions ◽  
Theta Functions ◽  
Mock Theta Functions ◽  
Third Order ◽  
Lost Notebook ◽  
Ramanujan's Lost Notebook

In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3) 4 (1954), 84–106), Yesilyurt (Four identities related to third order mock theta functions in Ramanujan’s lost notebook, Adv. Math. 190 (2005), 278–299) proved four identities for third order mock theta functions found on pages 2 and 17 in Ramanujan’s lost notebook. The primary purpose of this paper is to offer new proofs in the spirit of what Ramanujan might have given in the hope that a better understanding of the identities might be gained. Third order mock theta functions are intimately connected with ranks of partitions. We prove new dissections for two rank generating functions, which are keys to our proof of the fourth, and the most difficult, of Ramanujan’s identities. In the last section of this paper, we establish new relations for ranks arising from our dissections of rank generating functions.

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