Annales Mathematiques du Quebec最新文献

Let G be a semisimple compact connected Lie group. An N-fold reduced product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume of an N-fold reduced product of G. Suzuki and Takakura gave a volume formula for the N-fold reduced product of ( mathbf {SU}(3) ) in [25] by using geometric quantization and the Riemann–Roch formula. We compare our volume formula with theirs and prove that our volume formula agrees with theirs in the case of triple reduced products of ( mathbf {SU}(3) ).

This is a translation of the paper “Статистические  свойства  собственных  функций” which appeared in the Proceedings of the All-USSR School in Differential Equations with Infinite Number of Independent Variables and in Dynamical Systems with Infinitely Many Degrees of Freedom, Dilijan, Armenia, May 21–June 3, 1973; published by the Armenian Academy of Sciences, Yerevan, 1974. Translated from the Russian original by Semyon Dyatlov.

This article proves a case of the p-adic Birch and Swinnerton-Dyer conjecture for Garrett p-adic L-functions of [6], in the exceptional zero setting of extended analytic rank 2.

We discuss Shnirelman’s Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.

We study the algebraicity of the central critical values of twisted triple product L-functions associated to motivic Hilbert cusp forms over a totally real étale cubic algebra in the totally unbalanced case. The algebraicity is expressed in terms of the cohomological period constructed via the theory of coherent cohomology on quaternionic Shimura varieties developed by Harris. As an application, we generalize our previous result with Cheng on Deligne’s conjecture for certain automorphic L-functions for ({text {GL}}_3 times {text {GL}}_2).

Let (f(z)=q+sum _{nge 2}a(n)q^n) be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan J, 2021) for (k=2) by ruling out or locating all odd prime values (|ell |<100) of their Fourier coefficients a(n) when n satisfies some congruences. We also study the case of odd weights (kge 1) newforms where the nebentypus is given by a quadratic Dirichlet character.

On the canonical 2-sphere and for Schrödinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for every (pne 6), Sogge’s estimates by a power of the eigenvalue. This criterion can be formulated in terms of the critical points of the Radon transform of the potential and it is independent of the choice of eigenfunctions.

In a previous article [7], the author proves that the value of the root number varies in a non-isotrivial family of elliptic curves indexed by one parameter t running through ({mathbb {Q}}). However, a well-known example of Washington has root number (-1) for every fiber when t runs through ({mathbb {Z}}). Such examples are rare since, as proven in this paper, the root number of the integer fibers varies for a large class of families of elliptic curves. This result depends on the squarefree conjecture and Chowla’s conjecture, and is unconditional in many cases.

In this paper we consider the Diophantine equation (U_n=p^x) where (U_n) is a linear recurrence sequence, p is a prime number, and x is a positive integer. Under some technical hypotheses on (U_n), we show that, for any p outside of an effectively computable finite set of prime numbers, there exists at most one solution (n, x) to that Diophantine equation. We compute this exceptional set for the Tribonacci sequence and for the Lucas sequence plus one.