Ariel Pacetti

Newton–Hensel Interpolation Lifting

AbstractThe main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in ℤ[x] from information modulo a prime number p ≠ 2 to a power pk for any k, and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton--Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p-adic integers ℤp. Finally, we apply our results to sparse polynomial interpolation in ℤ[x].

Heegner Points on Cartan Non-split Curves

Let

Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields

E

MODULARITY OF THE CONSANI-SCHOLTEN QUINTIC

be an elliptic curve of conductor

Congruences between modular forms modulo prime powers

N

Anticyclotomic p-adic L-functions for additive reduction primes

, and let

On the number of Galois orbits of newforms.

K

Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes

be an imaginary quadratic field such that the root number of

HEEGNER POINTS CONSTRUCTION FOR RAMIFIED ADDITIVE REDUCTION PRIMES

E/K

Connectedness of Hecke Algebras and the Rayuela conjecture: a path to functoriality and modularity

is