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6 papers · 2 filters
Toy models for D. H. Lehmer's conjecture
Eiichi Bannai, Tsuyoshi Miezaki
In 1947, Lehmer conjectured that the Ramanujan -function never vanishes for all positive integers , where the are the Fourier coefficients of the cusp form $Δ_{…
Torsion points of abelian varieties with values in infinite extensions over a p-adic field
Yoshiyasu Ozeki
Let be an abelian variety over a -adic field and an algebraic infinite extension over . We consider the finiteness of the torsion part of the group of rational po…
Lifting Galois representations over arbitrary number fields
Yoshiyuki Tomiyama
It is proved that every two-dimensional residual Galois representation of the absolute Galois group of an arbitrary number field lifts to a characteristic zero -adic representat…
Smallness of fundamental groups for arithmetic schemes
Shinya Harada, Toshiro Hiranouchi
The smallness is proved of fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the Hermite-Minkowski theorem. We also refer to the case of varieties…
A note on evaluations of multiple zeta values
Shuichi Muneta
Multiple zeta values (MZVs) with certain repeated arguments or certain sums of cyclically generated MZVs are evaluated as rational multiple of powers of . In this paper, we gi…
On a ramification bound of torsion semi-stable representations over a local field
Shin Hattori
For a rational prime p, let k be a perfect field of characteristic p, K be a finite totally ramified extension of Frac(W(k)) of degree e and r be a non-negative integer satisfying…