Maass Spezialschar of level N

In this paper the image of the Saito-Kurokawa lift of level $N$ with Dirichlet character is studied. We give a new characterization of this so called Maass Spezialschar of level $N$ by symmetries involving Hecke operators related to $\Gamma_0(N)$. We finally obtain for all prime numbers $p$ local Maass relations. This generalizes known results for level $N=1$

Symmetric square L-values and dihedral congruences for cusp forms

AbstractLet p≡3(mod4) be a prime, and k=(p+1)/2. In this paper we prove that two things happen if and only if the class number h(−p)>1. One is the non-integrality at p of a certain trace of normalised critical values of symmetric square L-functions, of cuspidal Hecke eigenforms of level one and weight k. The other is the existence of such a form g whose Hecke eigenvalues satisfy “dihedral” congruences modulo a divisor of p (e.g. p=23, k=12, g=Δ). We use the Bloch–Kato conjecture to link these two phenomena, using the Galois interpretation of the congruences to produce global torsion elements which contribute to the denominator of the conjectural formula for an L-value. When h(−p)=1, the trace turns out always to be a p-adic unit

Polynominals related to powers of the Dedekind eta function

The vanishing properties of Fourier coefficients of integral powers of the Dedekind eta function correspond to the existence of integral roots of integer-valued polynomials Pn(x) introduced by M. Newman. In this paper we study the derivatives of these polynomials. We obtain non-vanishing results at integral points. As an application we prove that integral roots are simple if the index n of the polynomial is equal to a prime power pm or to pm + 1. We obtain a formula for the derivative of Pn(x) involving the polynomials of lower degree

Guidelines for a Space Propulsion Device Based on Heim's Quantum Theory

The text of the calligraphy on the front page means Cosmos, comprising the two chinese symbols for space and time. This calligraphy was done by Hozumi Gensho Roshi, Professor of Applied Sci-ences at Hanazono University, Kyoto, Japan in September 2003. The two red squares depict the sea