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تسجيل مستخدم جديدA characterization of modified mock theta functions
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We give a characterization of modified (in the sense of Zwegers) mock theta functions, parallel to that of ordinary theta functions. Namely, modified mock theta functions are characterized by their analyticity properties, elliptic transformation properties, and by being annihilated by certain second order differential operators.
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We show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra $hat{sell}_{2|1}$ (resp. $hat{psell}_{2|2}$) can be modified, using Zwegers real analytic corrections, to form a modular (resp. $S$-) invaria
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It is well known that the normaized characters of integrable highest weight modules of given level over an affine Lie algebra $hat{frak{g}}$ span an $SL_2(mathbf{Z})$-invariant space. This result extends to admissible $hat{frak{g}}$-modules, where $f
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We show that the normalized supercharacters of principal admissible modules, associated to each integrable atypical module over the affine Lie superalgebra $widehat{sl}_{2|1}$ can be modified, using Zwegers real analytic corrections, to form an $SL_2
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We study modular invariance of normalized supercharacters of tame integrable modules over an affine Lie superalgebra, associated to an arbitrary basic Lie superalgebra $ mathfrak{g}. $ For this we develop a several step modification process of multiv
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We study the parity of coefficients of classical mock theta functions. Suppose $g$ is a formal power series with integer coefficients, and let $c(g;n)$ be the coefficient of $q^n$ in its series expansion. We say that $g$ is of parity type $(a,1-a)$ i
f $c(g;n)$ takes even values with probability $a$ for $ngeq 0$. We show that among the 44 classical mock theta functions, 21 of them are of parity type $(1,0)$. We further conjecture that 19 mock theta functions are of parity type $(frac{1}{2},frac{1}{2})$ and 4 functions are of parity type $(frac{3}{4},frac{1}{4})$. We also give characterizations of $n$ such that $c(g;n)$ is odd for the mock theta functions of parity type $(1,0)$.
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