On fluctuations in the mean of a sum-of-divisors function
On fluctuations in the mean of a sum-of-divisors function, II
I give explicit values for the constant implied by an Omega-estimate due to Chen and Chen [CC] on the average of the sum of the divisors of n which are relatively coprime to any given integer a.
On formal groups obtained from symmetric powers
On formulas for the Frobenius number of a numerical semigroup.
On Fourier coefficients of modular forms of different weights
On Fourier coefficients of Siegel modular forms.
On Franel-Kluyver integrals of order three
On Fröhlich's Conjecture for Rings of Integers of Tame Extensions.
On Fully Split Lacunary Polynomials in Finite Fields
We estimate the number of possible degree patterns of k-lacunary polynomials of degree t < p which split completely modulo p. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory arguments.
On functional equations of complex powers.
On functions with bounded remainder
Let be a von Neumann-Kakutani - adic adding machine transformation and let . PutWe study three questions:1. When will be bounded?2. What can be said about limit points of 3. When will the skew product be ergodic on
On fundamental sets over a finite field.
On fundamental solutions of binary quadratic form equations
We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
On -discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences.
On galois automorphisms of the fundamental group of the projective line minus three points.
On Galois groups of p-closed algebraic number fields with restricted ramification II.
On Galois groups of p-closed algebraic number fields with restricted ramification.
On Galois isomorphisms between ideals in extensions of local fields.
On Galois representations arising from towers of coverings of P1 ... .
On Galois representations associated to Hilbert modular forms.