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- W2907448967 abstract "A bstract We define L-functions for meromorphic modular forms that are regular at cusps, and use them to: (i) find new relationships between Hurwitz class numbers and traces of singular moduli, (ii) establish predictions from the physics of T-reflection, and (iii) express central charges in two-dimensional conformal field theories (2d CFT) as a literal sum over the states in the CFTs spectrum. When a modular form has an order- p pole away from cusps, its q -series coefficients grow as n p −1 e 2 πnt for $$ tge frac{sqrt{3}}{2} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>t</mml:mi> <mml:mo>≥</mml:mo> <mml:mfrac> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> . Its L-function must be regularized. We define such L-functions by a deformed Mellin transform. We study the L-functions of logarithmic derivatives of modular forms. L-functions of logarithmic derivatives of Borcherds products reveal a new relationship between Hurwitz class numbers and traces of singular moduli. If we can write 2d CFT path integrals as infinite products, our L-functions confirm T-reflection predictions and relate central charges to regularized sums over the states in a CFTs spectrum. Equating central charges, which are a proxy for the number of degrees of freedom in a theory, directly to a sum over states in these CFTs is new and relies on our regularization of such sums that generally exhibit exponential (Hagedorn) divergences." @default.
- W2907448967 created "2019-01-11" @default.
- W2907448967 creator A5021483197 @default.
- W2907448967 date "2019-01-01" @default.
- W2907448967 modified "2023-10-12" @default.
- W2907448967 title "L-functions for meromorphic modular forms and sum rules in conformal field theory" @default.
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- W2907448967 doi "https://doi.org/10.1007/jhep01(2019)135" @default.
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