Kronecker’s first limit formula gives the polar and constant terms of the Laurent series expansion of the Eisenstein series for SL(2,Z) at s = 1. In this article, we generalize the formula to certain maximal parabolic Eisenstein series associated to SL(n,Z) for n ≥ 2.

We construct the p-adic standard L-functions for ordinary families of Hecke eigensystems of the symplectic group Sp(2n)/Q using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group Sp(4n)/Q, which guarantees the nonvanishing of local zeta integrals and allows us to p-adically interpolate the restriction...

In the case of an elliptic curve over a number field, this gives a criterion for the ‘integrality’ of Eisenstein symbol elements, and thus generalises a formula found by Bloch and Grayson [1986]. In the case of the universal elliptic curve, we obtain the boundary of the Eisenstein symbol at the cusps. (In characteristic zero an equivalent result was proved in [Beilinson 1986] by an analytic met...

where Bn, n ≥ 0, denotes the nth Bernoulli number, and where σν(n) = ∑ d|n d ν . The latter two representations in (1.1) can be established by using the Lipschitz summation formula or Fourier analysis. For these and other basic properties of Eisenstein series, see, for example, R. A. Rankin’s text [41, Chap. 6]. In Ramanujan’s notation, the three most relevant Eisenstein series are defined for ...

Introduction: This study aimed to investigate the effect of music on pain, anxiety and vital signs in children undergoing colonoscopy.   Method and Materials: This randomized study was carried out on 101 children (7 to 14 years old) requiring colonoscopy. Children were randomly allocated to a control or case group. The case group was played relaxing music (by Clayderman) during the procedure. S...

the aim of this study was to investigate the effect of different music rhythms on cardio respiratory responses during incremental exercises in young men. for this purpose, 17 non-athlete healthy males (ages: 19.76±0.97 yr, height: 176±6.72 cm, weight: 68.5±5.95 kg) voluntarily participated in this study. they performed bruce protocol until exhaustion with no music, slow music and fast music con...