Results 21 to 30 of about 12,785 (159)

Applications of an identity of Andrews

Arab Journal of Mathematical Sciences, 2014
In this paper, we give a bilateral form of an identity of Andrews, which is a generalization of the 1ψ1 summation formula of Ramanujan. Using Andrews’ identity, we deduce some new identities involving mock theta functions of second order and finally, we ...
D.D. Somashekara, K. Narasimha Murthy
doaj   +1 more source

Holomorphic projections and Ramanujan’s mock theta functions [PDF]

Proceedings of the National Academy of Sciences, 2014
Significance Mock theta functions were introduced by Ramanujan in 1920. They have become a vivid area of research, and they continue to play important roles in different parts of mathematics and physics. In this paper, we extend the concept of holomorphic projection, which allows us to prove identities for the Fourier series coefficients of ...
Imamoğlu, Özlem, Raum, Martin, Richter, Olav K.   +2 more
openaire   +3 more sources

Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]

, 2013
We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications.
Ahlgren, Scott, Kim, Byungchan
core   +1 more source

Unraveling the Morphological and Functional Maturation Mechanisms Underlying Human Neural Development Using iPSCs-Derived Neuronal Model. [PDF]

Adv Sci (Weinh)
Using human induced pluripotent stem cells (hiPSCs)‐derived neuronal model, Tian and colleagues reveal that voltage‐gated calcium channels Cav1.2 and Cav1.3, and their mediated calcium ion influx, are essential for early morphogenesis of human neuronal development, while ECEL1 underlies human neuronal functional developmental maturation through CALM3 ...
Tian Y, Ou YC, Zhang ZX, Cai J, Cai SQ, Xing GG.   +5 more
europepmc   +2 more sources

Asymptotic expansions, $L$-values and a new Quantum Modular Form [PDF]

, 2013
In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions ...
Costa, Edgar, Debaene, Korneel, Guerreiro, João   +2 more
core   +3 more sources

ON GENERALIZED EIGHTH ORDER MOCK THETA FUNCTIONS [PDF]

Ural Mathematical Journal, 2020
In this paper we have  generalized eighth order mock theta functions, recently introduced by Gordon and MacIntosh involving four independent variables. The idea of generalizing was to have four extra parameters, which on specializing give known functions and thus these results hold for those known functions.
openaire   +4 more sources

Modeling the angular correlation function and its full covariance in Photometric Galaxy Surveys [PDF]

, 2011
Near future cosmology will see the advent of wide area photometric galaxy surveys, like the Dark Energy Survey (DES), that extent to high redshifts (z ~ 1 - 2) but with poor radial distance resolution.
Cabre, Anna, Crocce, Martin, Gaztañaga, Enrique   +2 more
core   +2 more sources

Partition Identities for Ramanujan's Third Order Mock Theta Functions

, 2010
We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions $\phi(-q)$ and $\psi(-q)$. We also give an involution for Fine's partition identity on the mock theta function f(q).
Chen, William Y. C., Ji, Kathy Q., Liu, Eric H.   +2 more
core   +1 more source

D3-instantons, Mock Theta Series and Twistors [PDF]

, 2012
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial ...
A Dabholkar, A Haydys, A Karlhede, A Neitzke, A Swann, B Haghighat, B Pioline, B Wit de, B Wit de, Boris Pioline, C LeBrun, C Vafa, D Gaiotto, D Gaiotto, D Gaiotto, D Robles-Llana, D Robles-Llana, D Robles-Llana, DR Morrison, ER Sharpe, F Denef, F Saueressig, H Günther, I Antoniadis, I Antoniadis, J Bagger, J Boer de, J Boer de, J Boer de, J Manschot, J Manschot, J Manschot, J Manschot, J Manschot, J Troost, Jan Manschot, JM Maldacena, K Becker, K Becker, L Bao, L Göttsche, L Göttsche, M Bodner, M-F Vignéras, MR Douglas, NJ Hitchin, R Böhm, R Minasian, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Alexandrov, S Cecotti, S Ferrara, S Hosono, Sergei Alexandrov, SM Salamon, U Lindström   +66 more
core   +4 more sources

Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)

, 2012
By developing a connection between partial theta functions and Appell-Lerch sums, we find and prove a formula which expresses Hecke-type double sums in terms of Appell-Lerch sums and theta functions.
Andrews, Andrews, Andrews, Andrews, Andrews, Appell, Atkin, Berndt, Bringmann, Bringmann, Bruinier, Choi, Choi, Dean R. Hickerson, Eric T. Mortenson, Folsom, Gordon, Griffiths, Hecke, Hickerson, Hickerson, Kac, Kac, Kac, Lerch, McIntosh, Polishchuk, Ramanujan, Rogers, Schilling, Tannery, Watson, Zagier, Zwegers   +33 more
core   +1 more source