On the multidimensional zeta functions associated with theta functions, and the multidimensional Appell polynomials
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DOI: 10.1002/mma.6075
Abstract: We define and study the multidimensional Appell polynomials associated with theta functions. For the trivial theta functions, we obtain the various well‐known Appell polynomials. Many other interesting examples are given. To push our study, by… read more here.
Keywords: zeta functions; appell polynomials; multidimensional appell; theta functions ... See more keywords
Representations of mock theta functions
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DOI: 10.1016/j.aim.2020.107037
Abstract: Abstract Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized identities with two parameters a… read more here.
Keywords: representations mock; theta functions; lerch series; mock theta ... See more keywords
Degenerate Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation and the degenerate rational case
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DOI: 10.1016/j.geomphys.2020.104059
Abstract: Abstract We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tend to points, to get solutions to the KdV equation given… read more here.
Keywords: theta functions; riemann theta; degenerate; solutions kdv ... See more keywords
VANISHING COEFFICIENTS IN QUOTIENTS OF THETA FUNCTIONS OF MODULUS FIVE
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DOI: 10.1017/s0004972720000271
Abstract: Following recent investigations of vanishing coefficients in infinite products, we show that such instances are very rare when the infinite product is among a family of theta-quotients of modulus five. We also prove that a… read more here.
Keywords: theta functions; coefficients quotients; vanishing coefficients; modulus five ... See more keywords
Ramanujan’s theta functions and sums of triangular numbers
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DOI: 10.1142/s1793042119500520
Abstract: Let [Formula: see text] and [Formula: see text] be the set of integers and the set of positive integers, respectively. For [Formula: see text] let [Formula: see text] be the number of representations of [Formula:… read more here.
Keywords: theta functions; see text; formula see; ramanujan theta ... See more keywords