On the existence of a density
On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer.
On the existence of cusp forms over function fields.
On the existence of dimension zero divisors in algebraic function fields defined over
On the existence of Minkowski units in totally real cyclic fields
Let be a totally real cyclic number field of degree that is the product of two distinct primes and such that the class number of the -th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for .
On the existence of supersingular curves of given genus.
On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.
On the existence of uniformly distributed sequences in compact spaces
On the expansion of Fibonacci and Lucas polynomials.
On the Exponent Average of Integer Sequences.
On the exponent of the ideal class groups of imaginary extensions of
On the exponential diophantine equation
For any positive integer which is not a square, let be the least positive integer solution of the Pell equation and let denote the class number of binary quadratic primitive forms of discriminant . If satisfies and , then is called a singular number. In this paper, we prove that if is a positive integer solution of the equation with , then maximum and both , are singular numbers. Thus, one can possibly prove that the equation has no positive integer solutions .
On the exponential Diophantine equations of the form .
On the Exponential Divisor Function
On the exponential local-global principle
Skolem conjectured that the "power sum" A(n) = λ₁α₁ⁿ + ⋯ + λₘαₘⁿ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by α₁,...,αₘ is of rank 1.
On the extendability of elliptic surfaces of rank two and higher
We study threefolds having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not hyperplane section of a locally complete intersection threefold and we give some conditions, for many embeddings...
On the extendibility of the Diophantine triple .
On the extension of the Diophantine pair in .
On the ...-factor attached to motives.
On the Factorization of p-adic L-series.