Related papers: A possible generalization of Maeda's conjecture

Haj\'os' conjecture states that an Eulerian graph of order n can be decomposed into at most (n-1)/2 edge-disjoint cycles. We describe preprocessing steps, heuristics and integer programming techniques that enable us to verify Haj\'os'…

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden,…

This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.

We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.

In this article, we give a natural geometric interpretation of Kirillov's conjecture for tempered representations in the framework of orbit method. This interpretation can also be considered as a first generalization of Duflo's conjecture…

We solve the inverse Galois problem for del Pezzo surfaces of degree 1 over finite fields completely for 85 of the 112 possible types. We also determine for all 112 types the smallest field of existence. As an aside, we provide an example…

In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are new. No previous knowledge on the theory of valuations is…

We consider the set of classical newforms with rational coefficients and no complex multiplication. We study the distribution of quadratic-twist classes of these forms with respect to weight $k$ and minimal level $N$. We conjecture that for…

Let p be a prime and F a totally real field in which p is unramified. We consider mod p Hilbert modular forms for F, defined as sections of automorphic line bundles on Hilbert modular varieties of level prime to p in characteristic p. For a…

In this note by using elementary considerations, we settle Fr\"oberg's conjecture for a large number of cases, when all generators of ideals have the same degree.

Building on lifting results of Ramakrishna, Khare and Ramakrishna proved a purely Galois-theoretic level-raising theorem for two-dimensional odd representations of the Galois group of Q. In this paper, we generalize these techniques from…

In this mostly expository note, we explain a proof of Tate's two conjectures [Tat65] for algebraic cycles of arbitrary codimension on certain products of elliptic curves and abelian surfaces over number fields.

We introduce the new notion of the "quasi-Galois point" in Algebraic geometry, which is a generalization of the Galois point. A point $P$ in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial…

We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.

This paper presents a new characterisation of the Fermat curve, according to the arrangement of Galois points.

We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on classical slopes and more recent conjectures on slopes "at the…

We establish a geometrisation of the Breuil-M\'ezard conjecture for potentially Barsotti-Tate representations, as well as of the weight part of Serre's conjecture, for moduli stacks of two-dimensional mod p representations of the absolute…

This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.

These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.

A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an…