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.
Bad(s,t) is hyperplane absolute winning
J. An proved that for any s,t ≥ 0 such that s + t = 1, Bad (s,t) is (34√2)¯¹-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad (s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad (s,t) intersected with certain fractals.
Baker's explicit abc-conjecture and applications
Banach algebra techniques in the theory of arithmetic functions
For infinite discrete additive semigroups we study normed algebras of arithmetic functions endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.
Banach-Hecke algebras and -adic Galois representations.
Barnes' identities and representations of GL (2). I. Finite field case.
Barnes' identities and representations of GL (2). II. Nonarchimedian local field case.