We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary, orthogonal, or symplectic matrices, where the mom...

We obtain second integral moments of automorphic L–functions on adele groups GL2 over arbitrary number fields, by a spectral decomposition using the structure and representation theory of adele groups GL1 and GL2. This requires complete reformulation of the notion of Poincaré series, replacing the collection of classical Poincaré series over GL2(Q) or GL2(Q(i)) with a single, coherent, global o...

Abstract. We give a new heuristic for all of the main terms in the integral moments of various families of L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary, orthogonal, or symplectic matrices, where the mom...

In Ref. [1] Groote and Pivovarov have given notice of a possible fault in the use of sum rules involving two–point correlation functions to extract information on heavy quark parameters, due to the presence of massless contributions that invalidate the construction of moments of the spectral densities. Here we show how to circumvent this problem through a new definition of the moments, providin...

This review examines current eeorts to nd nd and exploit more powerful methods of measurement of the magnetic elds of the Ap stars. The methods now being explored include (1) the measurement of various moments of spectral lines in intensity and polarization spectra, and their interpretation in terms of moments of the observed elds, and (2) eld mapping by direct comparison of synthesized lines w...

The total n-electron energy of phenylenes is approximated by means of a linear combination of the fi rst few spectral moments of both molecular and line graphs. The two sets of moments produce very similar results, with very high accuracy. It is found that over 99.8% of the HMO totaln-electron energy of phenylenes is determined by the number of carbon atoms. Number of bay regions plays a signif...