When o has larger class number, linear combinations of CM-point values corresponding to the ideal classes yield the corresponding ratio. This example was understood in the 19th century, and is the simplest in well-known families of special values and periods of Eisenstein series. The next case in order of increasing complexity is that of integrals of the same Es along hyperbolic geodesics in H ...

We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of noncompact type, with K the maximal compact subgroup of G(R). In particular, we show ...

Automorphic forms are generalizations of periodic functions; they are functions on a group that are invariant under a discrete subgroup. A natural way to arrange this invariance is by averaging. Eisenstein series are an important class of functions obtained in this way. It is possible to give explicit formulas for their Fourier coefficients. Such formulas can provide clues to deep connections w...

this paper examines edward said’s views on music and its connection with key concepts such as orientalism and worldliness in his writings. it is suggested that to see the importance of classical western music as a key component of western culture in said’s work, one has to take into account the centrality of culture in his critical views and the stress he puts on its complicity with western imp...

the aim of this study was to investigate the effect of moderate rhythm of music on perceived exertion and heart rate during different intensities of endurance training in young male athletes. 10 male athletic students (mean + sd age 21.6±2.60 years) were voluntarily selected. the present study was conducted in a crossover design with and without music. the results showed no significant differen...

We develop an algorithm for numerical computation of the Eisenstein series on a Riemann surface of constant negative curvature. We focus in particular on the computation of the poles of the Eisenstein series. Using our numerical methods, we study the spectrum of the Laplace–Beltrami operator as the surface is being deformed. Numerical evidence of the destruction of Γ0(5)-cusp forms is presented.

We provide an explicit formula for the period integral of the unramified Eisenstein series on GL3(AQ) over the orthogonal subgroup associated with the identity matrix. The formula expresses the period integral as a finite sum of products of double Dirichlet series that are Fourier coefficients of Eisenstein series on the metaplectic double cover of GL3.

We locate almost all the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.

Introduction . . . . . . . . . $ 1. The problem . . . . . . . . . $2. Residues of cuspidal Eisenstein series 83. Exponents . . . . . . . . . $4. A comparison between two groups . $5. A property of the truncation operator $6. The constant terms of Eisenstein series $7. The negative dual chamber . . . . $8. Coefficients of the zero exponents . . $9. Conclusion . . . . . . . . . Bibliography . . ....