Some new mock theta functions
WebJan 1, 2011 · A.K. Agarwal, n-color partition theoretic interpretation of some mock theta functions, Electron. J. Combin. 11 (2004), no. 1, Note 14, 6pp (electronic). Google Scholar … WebHere, we modify his definition to include half-integral weights k and multiplier systems (γ ).)[43], a weight k quantum modular form is a complex-valued function f on 1 \ = a b ∈ Q, …
Some new mock theta functions
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WebNov 19, 2024 · Specializing the choices of $(a,b)$, we not only give various known and new representations for the mock theta functions of orders 2, 3, 5, 6 and 8, but also present … WebRamanujan’s first example of a mock theta function is the Eulerian series 2 X X qn (12) f (q) = 1 + a (n)qn = 1 + , (1 + q)2 (1 + q2)2 ··· (1 + qn)2 n≥1 n≥1 which appears deceptively …
WebJul 22, 2024 · Motivated by recent correlations between $ q $-series and mock theta functions, we establish a new $ q $-series transformation formula and derive the double … Web8 hours ago · I am trying to figure out how to pass a mock boto3 client to init.py with pytest, but am having some trouble. When I pass my fixture into the function I'm trying to test, the function called in init.py still tries to use a real instance of the boto client when get_secret is called instead of the one I'm mocking.
WebJun 29, 2005 · Three-manifold quantum invariants and mock theta functions. This proceeding highlights a new area where mock modular forms start to play an important … WebOct 1, 2024 · Mock theta functions can be represented by Eulerian forms, Hecke-type double sums, Appell–Lerch sums, and Fourier coefficients of meromorphic Jacobi forms. In view …
WebJan 24, 2024 · As of a few years ago, a fundamental question from Ramanujan's last letter remained, on a certain asymptotic relationship between mock theta functions and …
WebThe second point is that all 17 of Ramanujan’s mock theta functions were given in the form of q-hypergeometric series. (We recall that a q-hypergeometric series is a sum of the form … csr dissertation methodologyWebThe mock theta functions made their first appearance inRamanujan’s last letter to Hardy. Ramanujan explains that he is tryingto find functions apart from the... ean number state of michiganWeb2) and proved that 𝒟 5 ( 𝑞) is a mock theta function and called it of “2nd” order. He further showed that 𝒟 5 ( 𝑞) is a sum of two mock theta functions ℎ 1 ( 𝑞) and 𝜔 ( 𝑞) where ℎ 1 ( 𝑞) is of … csr distinguished namehttp://ramanujaninstitute.com/General/Mock%20theta%20Functions.pdf ean nummer gasWebIn 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) … csrd issbWeb1 day ago · Julian Catalfo / theScore. The 2024 NFL Draft is only two weeks away. Our latest first-round projections feature another change at the top of the draft, and a few of the marquee quarterbacks wait ... ean nummer formatWebJan 9, 2001 · A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q -series expansions. … ean number chemistry