Mock theta functions

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August undefined, 2024

WebThe extended results allow us to produce Hecke type series for the fifth and seventh order mock theta functions. New results on the generating function for sums of three squares also follow, and a new proof that every integer is the sum of three triangular numbers is given. References Similar Articles Additional Information Web1 okt. 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 of some q -series identities, we establish three two-parameter mock theta functions, and express them in terms of Appell-Lerch sums.

A Mock Theta Function of Second Order - Hindawi

WebInterpretations of four mock theta functions are obtained by attaching weights to the partitions generated by their unsigned versions. Further, mappings are established... View On mock theta... Web17 okt. 2014 · More mock theta functions were discovered afterward, including some of the 10th order [2, 3]. A variety of applications appear in the fields of hypergeometric functions, number theory, Mordell integrals, probability theory, and mathematical physics, where they are used to determine critical dimensions in some string theories. pcast organizational chart

AMS :: Transactions of the American Mathematical Society

http://lovejoy.perso.math.cnrs.fr/ WebIn mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and … Webyears, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” pcast wildland fire

Representations of mock theta functions - Semantic Scholar

RAMANUJAN’S MOCK THETA FUNCTIONS AND THEIR …

Web27 nov. 2006 · Previously, the author proved six of the eight tenth order mock theta function identities. It is the purpose of this paper to prove the fifth and sixth identities of Ramanujan's tenth order mock theta functions. The properties of modular forms are used for the proofs of theta function identities. 1. Introduction Webpaper we focus only on Ramanujan’s mock theta functions. The Metaplectic Cover and Quasimodular Forms We briefly introduce some standard notation needed for the … scripture where were you when iWeb9 dec. 2024 · Mock theta functions appeared out of the blue in Ramanujan's last letter to Hardy. What would lead Ramanujan to consider the possibility of such functions in the first place? This paper seeks to provide a plausible answer to this question. scripture while sleeping

"Web21 dec. 2024 · In 1991, Andrews and Hickerson established a new Bailey pair and combined it with the constant term method to prove some results related to sixth-order mock theta … " - Mock theta functions

Mock theta functions

AMS :: Transactions of the American Mathematical Society

Web3 mrt. 2014 · 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 … WebMock Theta Conjectures. The proof of these and others for mock theta functions of seventh order were given by Hickerson [21], [22]. See [1] for a wide-ranging survey and references on such problems (i.e. of the rst type) about mock theta functions. Ramanujan emphasized that a mock theta function should not have the same singularities

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Web20 aug. 2012 · This family of special forms and another closely related family of weight-one forms contain almost all the known mock modular forms including the mock theta functions of Ramanujan, the generating function of Hurwitz-Kronecker class numbers, the mock modular forms appearing in the Mathieu and Umbral moonshine, as well as an … WebMock theta functions and Appell-Lerch sums . doi: 10.1186/s13660-018-1748-1. Epub 2024 Jul 3. Author Bin Chen 1 2 Affiliations 1 1School of Mathematics, Shandong University, Jinan, China. 2 2School of Mathematics and Physics, Weinan Normal University, Weinan, China. PMID: 30137884 PMCID: PMC6061538 DOI: 10.1186/s13660-018-1748-1

Web13 mei 2024 · Since then, mock theta functions have attracted the attention of many mathematicians. It was some time before researchers understood the modularity of mock theta functions. From the Eulerian forms of mock theta functions, it is difficult to observe any significant transformation properties. Web17 okt. 2014 · More mock theta functions were discovered afterward, including some of the 10th order [2, 3]. A variety of applications appear in the fields of hypergeometric …

WebRamanujan. The ﬁrst paper considers only the third-order functions. It provides three new mock ϑ-functions not mentioned in the letter. The bulk of the paper is devoted to the … Web24 jan. 2024 · Asymptotics and Ramanujan's mock theta functions: then and now Asymptotics and Ramanujan's mock theta functions: then and now Philos Trans A Math Phys Eng Sci. 2024 Jan 24;378 (2163):20240448. doi: 10.1098/rsta.2024.0448. Epub 2024 Dec 9. Author Amanda Folsom 1 Affiliation 1 Mathematics and Statistics, Amherst …

In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1/2. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Sander Zwegers discovered that adding certain non-holomorphic functions to them turns them into harmonic weak Maass forms.

Webthere are linear relations among the mock theta functions (here, ˚= f+ 2 ); the space they span contains a subspace of ordinary modular forms; one must multiply by suitable … pc astuces firefox 64 bitsWeb15 nov. 2024 · Mock theta functions were first introduced by Ramanujan. Historically, mock theta functions can be represented as Eulerian forms, Appell-Lerch sums, Hecke-type double sums, and Fourier coefficients of meromorphic Jacobi forms. scripture whom shall i sendWeb9 jan. 2001 · Abstract. A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q … pcast working groupWebThe mock theta functions were named and first studied by S. Ramanujan. Four months before he died, he sketched his results in a letter to G. H. Hardy [14, pp. 354-355]. The results in this letter formed the basis on … scripture while sleeping youtubeWebDelta Sigma Pi - Theta Chi Chapter. May 2024 - Dec 20248 months. San Jose, California, United States. - Focused on fundraising for charities … pcast wildfireWebIf `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x os equal to `underlinebb(sqrt(145)/12)`. Explanation: `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2;(x > 3/4)` scripture where your treasure isWebSuppose that is one of Ramanujan’s alleged examples of a mock theta function. Then, there are integers γ and δ for which is the holomorphic part of the weight 1/2 harmonic … scripture where your heart is