Weyl group multiple Dirichlet series constructed from quadratic characters

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are the first examples of an infinite collection of unstable Weyl group multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment

Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards

Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.Comment: 18 pages, 10 figure

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde

Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

Ghrelin and its Association with Nutritional and Inflammatory Status of Patients on Maintenance Hemodialysis in a South Indian Tertiary Care Hospital

Background: Malnutrition and inflammation are associated with morbidity and mortality in patients on maintenance hemodialysis (MHD). Ghrelin, an orexigenic peptide hormone, is speculated to be associated with nutritional and inflammatory status in MHD. Aim: To assess the serum total ghrelin levels and its possible relationship with inflammation and nutritional status in patients on MHD. Subjects and Methods: The study was conducted on 90 patients on MHD for 6 months and above (56 males, 34 females, mean age 52.6 [11.7] years; mean dialysis vintage 20.9 [12.1] months) and 70 healthy volunteers as control (5 males, 25 females, mean age 50.6 [9.7] years). Demographics were obtained for the study population, and dialysis‑related data were collected for cases. Anthropometry, biochemical parameters, serum total ghrelin and inflammatory markers tumor necrosis factor‑alpha (TNF‑α), and high‑sensitivity C‑reactive protein (hsCRP) were assessed for cases and control. Self‑reported appetite (five questions of appetite and diet assessment tool) and nutritional status (subjective global assessment‑dialysis malnutrition score) were assessed for cases. Results: Ghrelin (242.5 [62.3] pg/mL vs. 80.2 [19.6] pg/mL; P < 0.001), TNF‑α (39.8 [15.2] pg/mL vs. 6.5 [1.2] pg/mL; P < 0.001), hsCRP (10.2 [2.8] mg/L vs. 2.7 [0.54] mg/L; P < 0.001) were significantly elevated in cases versus control, anthropometry, and biochemical parameters were significantly decreased in hemodialysis patient. Of 90 cases, (13/90 [14.4%]) were well‑nourished, (28/90 [31%]) mild to moderately malnourished, and (49/90 [54.4%]) were moderate to severely malnourished. Appetite was very good for 14.4%, good and fair for 47.8%, poor and very poor for 37.8% patients. There was a significant difference in appetite with respect to nutritional status (P < 0.001). Ghrelin had positive correlation with inflammatory markers and negative correlation with nutritional status (P < 0.001). Conclusion: The study identified the association of ghrelin with appetite, nutritional, and inflammatory status of the patients on MHD.Keywords: Appetite, Ghrelin, Hemodialysis, Inflammation, Nutritional statu