Scalar Virasoro primaries in any 2d CFT obey a crossing equation whose high-temperature form is controlled by a modular integral and by oscillations tied to the nontrivial zeros of the Riemann zeta function.
Higher $d$ Eisenstein Series and a Duality-Invariant Distance Measure
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The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product $E_s(G,B)$ of the real analytic Eisenstein series $E_s(\tau, \bar{\tau})$ and a general point in Narain moduli space. We also discuss the utility of the Petersson inner product as a distance measure on the space of 2d CFTs, and apply our procedure to evaluate this distance in various examples.
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Properties of scalar partition functions of 2d CFTs
Scalar Virasoro primaries in any 2d CFT obey a crossing equation whose high-temperature form is controlled by a modular integral and by oscillations tied to the nontrivial zeros of the Riemann zeta function.