Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periods of the $j$-function along infinite geodesics and mock modular
  forms   Zagier's well-known work on traces of singular moduli relates the
coefficients of certain weakly holomorphic modular forms of weight $1/2$ to
traces of values of the modular $j$-function at imaginary quadratic points. A
real quadratic analogue was recently studied by Duke, Imamo\=glu, and T\'oth.
They showed that the coefficients of certain weight $1/2$ mock modular forms \[
f_D = \sum_{d>0} a(d,D) q^d, \qquad D>0 \] are given in terms of traces of
cycle integrals of the $j$-function. Their result applies to those coefficients
$a(d,D)$ for which $dD$ is not a square. Recently Bruinier, Funke, and
Imamo\=glu employed a regularized theta lift to show that the coefficients
$a(d,D)$ for square $dD$ are traces of regularized integrals of the
$j$-function. In the present paper we provide an alternate approach to this
problem. We introduce functions $j_{m,Q}$ (for $Q$ a quadratic form) which are
related to the $j$-function and show, by modifying the method of Duke,
Imamo\=glu, and T\'oth, that the coefficients for which $dD$ is a square are
traces of cycle integrals of the functions $j_{m,Q}$.

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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th