The Schinzel hypothesis for polynomials

The Schinzel-Giedion syndrome.

On composite lacunary polynomials and the proof of a conjecture of Schinzel

Let g(x) be a fixed non-constant complex polynomial. It was conjectured by Schinzel that if g(h(x)) has boundedly many terms, then h(x) ∈ C[x] must also have boundedly many terms. Solving an older conjecture raised by Rényi and by Erdös, Schinzel had proved this in the special cases g(x) = x; however that method does not extend to the general case. Here we prove the full Schinzel’s conjecture (...

8. Davenport-schinzel Sequences

Definition 18.1 A (n, s)-Davenport-Schinzel sequence is a sequence over an alphabet A of size n in which no two consecutive characters are the same and there is no alternating subsequence of the form .

Riemann hypothesis for period polynomials of modular forms.

The period polynomial r(f)(z) for an even weight k≥4 newform f∈S(k)(Γ(0)((N)) is the generating function for the critical values of L(f,s) . It has a functional equation relating r(f)(z) to r(f)(-1/Nz). We prove the Riemann hypothesis for these polynomials: that the zeros of r(f)(z) lie on the circle |z|=1/√N . We prove that these zeros are equidistributed when either k or N is large.

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...