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An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors

Amit Hogadi, Supriya Pisolkar (2013)

Acta Arithmetica

Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension k L / k K is separable. For an integer n ≥ 0, let W n ( L ) denote the ring of Witt vectors of length n with coefficients in L . We show that the proabelian group H 1 ( G , W n ( L ) ) n ∈ ℕ is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.

An example in Beurling's theory of generalised primes

Faez Al-Maamori, Titus Hilberdink (2015)

Acta Arithmetica

We prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes. The example has its generalised Chebyshev function given by [x]-1, and associated zeta function ζ₀(s) given via - ( ζ ' ₀ ( s ) ) / ( ζ ₀ ( s ) ) = ζ ( s ) - 1 , where ζ is Riemann’s zeta function. We study the behaviour of the corresponding Beurling integer counting function N(x), producing O- and Ω- results for the ’error’ term. These are strongly influenced by the size of ζ(s) near...

An exercise on Fibonacci representations

Jean Berstel (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.

An explicit algebraic family of genus-one curves violating the Hasse principle

Bjorn Poonen (2001)

Journal de théorie des nombres de Bordeaux

We prove that for any t ∈ 𝐐 , the curve 5 x 3 + 9 y 3 + 10 z 3 + 12 t 2 + 82 t 2 + 22 3 ( x + y + z ) 3 = 0 in 𝐏 2 is a genus 1 curve violating the Hasse principle. An explicit Weierstrass model for its jacobian E t is given. The Shafarevich-Tate group of each E t contains a subgroup isomorphic to 𝐙 / 3 × 𝐙 / 3 .

An explicit computation of p -stabilized vectors

Michitaka MIYAUCHI, Takuya YAMAUCHI (2014)

Journal de Théorie des Nombres de Bordeaux

In this paper, we give a concrete method to compute p -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over p -adic fields. An application to the global setting is also discussed. In particular, we give an explicit p -stabilized form of a Saito-Kurokawa lift.

Currently displaying 1421 – 1440 of 16591