Jörg Jahnel

most citedWhen is the (co)sine of a rational angle equal to a rational number?

25 citations · 33 across the 6 of their papers we have counts for

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math.NT2010

More cubic surfaces violating the Hasse principle

Jörg Jahnel

We generalize L.J. Mordell's construction of cubic surfaces for which the Hasse principle fails.

math.NT2010

The Diophantine Equation $x^{4} + 2 y^{4} = z^{4} + 4 w^{4}$ ---a number of improvements

Andreas-Stephan Elsenhans, Jörg Jahnel

The quadruple $(1484801, 1203120, 1169407, 1157520)$ already known is essentially the only non-trivial solution of the Diophantine equation $x^4 + 2 y^4 = z^4 + 4 w…

math.NT2010

The Fibonacci sequence modulo $p^{2}$ -- An investigation by computer for $p < 1 0^{14}$

Andreas-Stephan Elsenhans, Jörg Jahnel

We show that for primes $p < 1 0^{14}$ the period length $κ (p^{2})$ of the Fibonacci sequence modulo $p^{2}$ is never equal to its period length modulo $p$ . The investigation involves a…

math.NT2010★ 5 cited

The discriminant of a cubic surface

Andreas-Stephan Elsenhans, Jörg Jahnel

We construct explicit examples of cubic surfaces over $Q$ such that the 27 lines are acted upon by the index two subgroup of the maximal possible Galois group. This is the simpl…

More cubic surfaces violating the Hasse principle

The Diophantine Equation x4+2y4=z4+4w4---a number of improvements

The Fibonacci sequence modulo p2 -- An investigation by computer for p<1014

The discriminant of a cubic surface

The Diophantine Equation $x^{4} + 2 y^{4} = z^{4} + 4 w^{4}$ ---a number of improvements

The Fibonacci sequence modulo $p^{2}$ -- An investigation by computer for $p < 1 0^{14}$