New theta function identities for a continued fraction of Ramanujan and their applications
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DOI: 10.1007/s13370-020-00823-z
Abstract: We prove three new theta function identities for the continued fraction H ( q ) defined by $$\begin{aligned} H(q):=q^{1/8}-\frac{q^{7/8}}{1-q}_{+}\frac{q^2}{1+q^2}_{-}\frac{q^3}{1-q^3}_{+}\frac{q^4}{1+q^4}_{- \cdots }, \vert q\vert read more here.
Keywords: function identities; theta function; continued fraction; new theta ... See more keywords
Romik's conjecture for the Jacobi theta function
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DOI: 10.1016/j.jnt.2020.01.009
Abstract: Dan Romik recently considered the Taylor coefficients of the Jacobi theta function around the complex multiplication point $i$. He then conjectured that the Taylor coefficients $d(n)$ either vanish or are periodic modulo any prime ${p}$;… read more here.
Keywords: jacobi theta; theta function; romik conjecture; conjecture jacobi ... See more keywords
ARITHMETIC PROPERTIES OF COEFFICIENTS OF THE MOCK THETA FUNCTION $B(q)$
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DOI: 10.1017/s0004972719001175
Abstract: We investigate the arithmetic properties of the second-order mock theta function $B(q)$ and establish two identities for the coefficients of this function along arithmetic progressions. As applications, we prove several congruences for these coefficients. read more here.
Keywords: properties coefficients; theta function; mock theta; coefficients mock ... See more keywords
A mock theta function identity related to the partition rank modulo 3 and 9
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DOI: 10.1142/s1793042120400254
Abstract: We prove a new mock theta function identity related to the partition rank modulo 3 and 9. As a consequence, we obtain the [Formula: see text]-dissection of the rank generating function modulo [Formula: see text].… read more here.
Keywords: theta function; mock theta; identity related; rank ... See more keywords