Using a method of H. Davenport and W. M. Schmidt, we show that, for each positive integer n, the ratio 2/n is the optimal exponent of simultaneous approximation to real irrational numbers 1) by all conjugates of algebraic numbers of degree n, and 2) by all but one conjugates of algebraic integers of degree n + 1.

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are h...

We look at genera of even unimodular lattices rank 12 over the ring integers $${{\mathbb {Q}}}(\sqrt{5})$$ and 8 {Q}}}(\sqrt{3})$$ , using Kneser neighbours to diagonalise spaces scalar-valued algebraic modular forms. conjecture most global Arthur parameters, prove several them theta series, in manner Ikeda Yamana. find instances congruences for non-parallel weight Hilbert Turning genus Hermiti...

There is a well-known formula due to Andrews that counts the number of incongruent triangles with integer sides and a fixed perimeter. In this note, we consider the analagous question counting the number of k-tuples of nonnegative integers none of which is more than 1/(k−1) of the sum of all the integers. We give an explicit function for the generating function which counts these k-tuples in th...

In this paper, we prove that ζ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in Γ(α),Γ(n),Γ(l) over the ring C, l>n>α≥0 nonnegative integers. We extend result does satisfy Γ,Γ′,Γ″ field complex numbers, which proved by Li and Ye [Li BQ, Z. Algebraic equations concerning Riemann zeta function Euler gamma function. Indiana Univ Math J. 201...

The moduli space of principally polarized abelian varieties $A_g$ genus g is defined over the integers and admits a minimal compactification $A_g^*$, also integers. Hodge bundle has its Chern classes in Chow ring with rational coefficients. We show that prime field $F_p$, these naturally lift to $A_g^*$ do so best possible way: despite highly singular nature they are represented by algebraic cy...