On the Rankin–Selberg Method for Functions Not of Rapid Decay on Congruence Subgroups

Gupta, Shamita Dutta

doi:10.1006/jnth.1997.2035

Cited by 6 publications

(7 citation statements)

References 2 publications

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“…Having defined the Eisenstein series for Γ 0 (N), we now turn to the evaluation of the integral (2.14) by following the unfolding procedure outlined in Section 3.2 (see also [26]). As already mentioned, in this case the integrand A N is a (not necessarily holomorphic) automorphic function of Γ 0 (N), with at most power-like growth at each cusp 5…”

Section: The Rankin-selberg Methods For Hecke Congruence Subgroupsmentioning

confidence: 99%

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Rankin-Selberg methods for closed strings on orbifolds

Angelantonj

Florakis

Pioline

2013

J. High Energ. Phys.

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In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus. Unlike the traditional approach, the Narain lattice does not play any role in the unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl chamber is not required and the analytic structure of the amplitude is transparent. In the present paper, we generalise this procedure to the case of Abelian Z N orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup Γ 0 (N ). As a result, the original modular integral reduces to an integral over the fundamental domain of Γ 0 (N ), which we then evaluate by extending our previous techniques. Our method is applicable, for instance, to the evaluation of one-loop corrections to BPS-saturated couplings in the low energy effective action of closed string models, of quantum corrections to the Kähler metric and, in principle, of the free-energy of superstring vacua.

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Section: The Rankin-selberg Methods For Hecke Congruence Subgroupsmentioning

confidence: 99%

“…Following a similar procedure, one finds 24) for N = 3, 25) for N = 4, and finally 26) for N = 6. The various integrals can then be computed using the results of the previous section.…”

Section: N = 2 Heterotic String Vacuamentioning

confidence: 99%

Rankin-Selberg methods for closed strings on orbifolds

Angelantonj

Florakis

Pioline

2013

J. High Energ. Phys.

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“…We now describe a different method for understanding R 1 (|E(z, w, 1/2)| 2 , s), namely Zagier's Rankin-Selberg method for functions not of rapid decay. This method was introduced by Zagier for the group SL 2 (Z) in [39] and generalized by Kudla (unpublished), Dutta Gupta [10], and Mizuno [23]. Its usefulness for determining the contribution of the incomplete Eisenstein series to the asymptotics can already be seen in [41].…”

Section: 2mentioning

confidence: 99%

Double Dirichlet series and quantum unique ergodicity of weight one-half Eisenstein series

Raulf

Risager

2014

Algebra Number Theory

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“…We now describe a different method for understanding R 1 |E(z, w, 1 2 )| 2 , s , namely Zagier's Rankin-Selberg method for functions not of rapid decay. This method was introduced by Zagier [1981] for the group SL 2 ‫)ޚ(‬ and generalized by Kudla (unpublished), Dutta Gupta [1997], and Mizuno [2005]. Its usefulness for determining the contribution of the incomplete Eisenstein series to the asymptotics can already be seen in [Zelditch 1991].…”

Section: Bmentioning

confidence: 99%