Results 1 to 10 of about 789 (103)
Mock theta functions and Appell–Lerch sums [PDF]
Journal of Inequalities and Applications, 2018 Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
doaj +8 more sources
Ramanujan's mock theta functions. [PDF]
Proc Natl Acad Sci U S A, 2013 In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function , and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268–277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the ...
Griffin M, Ono K, Rolen L.
europepmc +4 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
Pramod Kumar Rawat
doaj +4 more sources
Effective Congruences for Mock Theta Functions [PDF]
Mathematics, 2013 Let M(q) = ∑c(n) qn be one of Ramanujan’s mock theta functions. We establish the existence of infinitely many linear congruences of the form: c(An + B) ≡ 0 (mod lj) where A is a multiple of l and an auxiliary prime, p.
Heidi Goodson +3 more
doaj +4 more sources
Holomorphic projections and Ramanujan's mock theta functions. [PDF]
Proc Natl Acad Sci U S A, 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 Ö, Raum M, Richter OK.
europepmc +5 more sources
MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS [PDF]
Forum of Mathematics, Pi, 2013 Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM +2 more
doaj +2 more sources
Recurrence relations connecting mock theta functions and restricted partition functions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler's pentagonal number theorem, and Ramanujan's theta ...
M. Rana, H. Kaur, K. Garg
doaj +1 more source
Some Special Integer Partitions Generated by a Family of Functions
Trends in Computational and Applied Mathematics, 2023 In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define a collection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from
M. L. Matte
doaj +1 more source
On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds [PDF]
Royal Society Open Science, 2015 In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds.
Kathrin Bringmann +2 more
doaj +1 more source
Optimal mock Jacobi theta functions
Advances in Mathematics, 2020 We classify the optimal mock Jacobi forms of weight one with rational coefficients. The space they span is thirty-four-dimensional, and admits a distinguished basis parameterized by genus zero groups of isometries of the hyperbolic plane. We show that their Fourier coefficients can be expressed explicitly in terms of singular moduli, and obtain ...
Cheng, M.C.N., Duncan, J.F.R.
openaire +6 more sources