Related papers: The level 1 weight 2 case of Serre's conjecture

In this paper we prove a level raising theorem for some weight $2$ trivial character newforms at almost every prime $p$. This is done by ignoring the residue characteristic at which the level raising appears.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We settle in the affirmative the Graham-Sloane conjecture.

We obtain new partial results supporting the spectral set conjecture in dimension 1.

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

A proof of Smale's mean value conjecture from 1981 is given.

We give a new simpler proof of a theorem of Jayne and Rogers.

The article presents the proof of Casas-Alvero conjecture.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

In this paper we prove the WALA conjecture.

The main result can be given a short and elementary proof which has been incorporated into Lemma 3.2 of arXiv:1206.5775

In this short note, we expose some of the works on Serre intersection multiplicity conjecture. I provide a proof of the vanishing of Serre intersection multiplicity in non-proper intersection over a regular ring based on the intersection…

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

We show that the Jacobian conjecture of the two dimensional case is true.

We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the…

The well-known 1-2-3 Conjecture asserts that the edges of every graph without an isolated edge can be weighted with $1$, $2$ and $3$ so that adjacent vertices receive distinct weighted degrees. This is open in general. We prove that every…

In this note we prove a weighted version of the Khintchine inequalities.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

Several results about the union-closed sets conjecture are presented.

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.