On the average number of direct factors of a finite abelian group (“sur les variété abéliennes”)
On the average number of direct factors of finite abelian groups (II)
On the average number of unitary factors of finite abelian groups
On the average of character sums for a group of characters
On the average of inversion of Dirichlet’s -functions
On the behaviour close to the unit circle of the power series with Möbius function coefficients
Let . We prove that for each root of unity there is an a > 0 such that as r → 1-. For roots of unity e(l/q) with q ≤ 100 we prove that these omega-estimates are true with a = 1/2. From omega-estimates for (z) we obtain omega-estimates for some finite sums.
On the Bombieri-Korobov estimate for Weyl sums
On the Brun-Titchmarsh theorem.
On the class number of binary quadratic forms: An omega estimate for the error term.
On the constant factor in Vinogradov's Mean Value Theorem
On the cycle structure of linear recurring sequences.
On the degree of the -function associated with an exponential sum
On the determination of Gauss sums
On the determination of generalized Gauss sums
On the diaphony of some finite hybrid point sets
On the difference between a D. H. Lehmer number and its inverse modulo q
On the difference between consecutive squarefree integers
On the difference of the consecutive primitive roots
On the Dirichlet characters of polynomials in several variables
On the discrepancy of sequences associated with the sum-of-digits function
If denotes the sequence of best approximation denominators to a real , and denotes the sum of digits of in the digit representation of to base , then for all irrational, the sequence is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if has bounded continued fraction coefficients.