Average Frobenius distributions for elliptic curves over abelian extensions
Average Frobenius distributions for elliptic curves with nontrivial rational torsion
Average multiplicative orders of elements modulo n
Average order in cyclic groups
For each natural number we determine the average order of the elements in a cyclic group of order . We show that more than half of the contribution to comes from the primitive elements of order . It is therefore of interest to study also the function . We determine the mean behavior of , , , and also consider these functions in the multiplicative groups of finite fields.
Average orders of multiplicative arithmetical functions of integer matrices
Average r-rank Artin conjecture
Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups , with and , with a range of uniformity for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...
Average size of 2-Selmer groups of elliptic curves, II
Average Value of the Euler Function on Binary Palindromes
We study values of the Euler function φ(n) taken on binary palindromes of even length. In particular, if denotes the set of binary palindromes with precisely 2ℓ binary digits, we derive an asymptotic formula for the average value of the Euler function on .
Average values of L-series in function fields.
Averages of Euler products, distribution of singular series and the ubiquity of Poisson distribution
Averages of short exponential sums
Averages of short exponential sums, II
Averages of twisted elliptic L-functions
Aviezri Fraenkel's work in number theory.
: The vise tightens. (Ensembles : L'étau se resserre.)
-sequences whose terms are squares
-représentations dans le cas relatif
Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les -représentations. On donne des applications à la théorie des représentations -adiques, en la reliant à la théorie des -modules relatifs, et à celle des modules de Higgs -adiques développée par G. Faltings.
B₂[∞]-sequences of square numbers
Badly Approximable Formal Power Series.
Badly approximable systems of linear forms over a field of formal series
We prove that the Hausdorff dimension of the set of badly approximable systems of linear forms in variables over the field of Laurent series with coefficients from a finite field is maximal. This is an analogue of Schmidt’s multi-dimensional generalisation of Jarník’s Theorem on badly approximable numbers.