Theta Functions
Mock theta functions and Appell–Lerch sums
... mock theta functions were first introduced by Ramanujan in his last letter to Hardy [2, ...seventeen functions which he called mock theta functions [4, ...mock theta ...
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ON GENERALIZED EIGHTH ORDER MOCK THETA FUNCTIONS
... 17 functions and called them mock theta functions as they were not theta functions and classified them as 4 functions of third order, 10 functions of fifth order and 3 ...
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Some theorems on the explicit evaluation of Ramanujan's theta functions
... the identities can be found in [1]. However, in the unorganized pages of his notebooks [8], Ramanujan recorded many other beautiful identities. Proofs of these identities can be found in [2, 3]. In Section 2, we prove ...
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Properties of Certain Bilateral Mock Theta Functions-IV
... mock theta functions of order ...mock theta functions. The ‘Complete’ sixth order mock theta functions were studied by ...mock theta functions of order five, eight, ...
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Generating Functions for Generalized Mock Theta Functions
... mock theta functions namely 7, , F , H , I of Andrews ...generalized functions 7, , F and K reduce to the third order mock theta functions of Ramanujan and I , H and M to the third ...
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Some circular summation formulas for theta functions
... for theta functions (see []), but from one main result, Theorem of Liu, we do not deduce our results in the present ...of theta functions and find more interesting formulas (see, for ...
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Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki
... The theta-link involves two distinct ring/scheme theories, two theatres (see footnote 38) in the domain and codomain of the theta-link, with their multiplicative structures related via nonarchimedean ...
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Generalization for character formulas in terms of continued fraction identities
... = (q 20 , q 40 , q 60 ; q 60 ) ∞ (1.38) The outline of this paper is as follows. In sections 2, we have recorded some well known results on continued fraction identities and recent results on character formulas for mock ...
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Arithmetic on Abelian and Kummer Varieties
... 2 theta functions and we explain that by using differential and compatible additions it is possible to compute the fiber of the natural projection A → K A (from level 4 to level 2) up to one choice of ...
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Hilbert modular forms of weight 1/2
... In [Serre-Stark], Serre and Stark proved a theorem which gives explicit basis consisting of theta functions for some spaces of half integral weight modular forms.... 2 The Hilbert modula[r] ...
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Modern aspects of topological gauge theories Polynomial invariants and mock modular forms
... mock theta functions [93, 94]. An indefinite theta function Θ : H → C is a holomorphic q-series defined as a sum over an indefinite lattice Λ with signature (1, n − ...
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Galois action on special theta values
... (where ǫ = 0 for even χ, ǫ = 1 for odd χ) the associated theta series. Its value at its point of symmetry under the modular transformation τ 7→ − 1/τ is related by θ χ (i) = W (χ)θ χ ¯ (i) to the root number of ...
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Theta function identities from optical neural network transformations
... These functions are actu’,dly connected with a type of theta functions, the so-called nil-theta functions, which may be defined in a natural way on a Heisenberg compact nilmanifold see A[r] ...
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A new class of theta function identities in two variables
... Abstract. We describe a new series of identities, which hold for certain gen- eral theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta ...
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Vol 2, No 3 (2011)
... interesting functions recently which I called ‘Mock’ ...mock theta functions of third order, fifth order and seventh order together with identities satisfied by ...Mock theta functions ...
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Congruent number theta coefficients to 10¹²
... the theta functions being multiplied, LIMIT, and the optimal block size, BLOCK, for the computation of the theta coefficients were set (see the section on cache efficient computation of theta ...
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Modular relations and explicit values of Ramanujan Selberg continued fractions
... By employing a method of parameterizations for Ramanujan’s theta-functions, we find several modular relations and explicit values of the Ramanujan-Selberg continued fractions.. Copyright[r] ...
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Differential response of hippocampal and prefrontal oscillations to systemic LPS application
... low theta are significantly increased, while the high theta power values are significantly decreased compared to controls (Tamura et ...of theta oscillations seen in the hippocampal LFP (Geisler et ...
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Identification of Common Structural Motifs from Proteases, Kinases, and Phosphatases Using a New Structure Comparison Method
... Protein 3-D structures are more functionally conserved than sequence and this claims the need of developing a computational tool for accurate protein structure comparison at the global and local levels. We have developed ...
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Theta oscillations in 4-year-olds are sensitive to task engagement and task demands
... before children had to respond or the next part was initiated. More specifically, the same movie clip was repeated three times before a response was required. Before watching the action clips, children were instructed to ...
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