Results 11 to 20 of about 292 (50)

Rational points on Erdős–Selfridge superelliptic curves [PDF]

, 2015
Given k⩾2k⩾2, we show that there are at most finitely many rational numbers xx and y≠0y≠0 and integers ℓ⩾2ℓ⩾2 (with (k,ℓ)≠(2,2)(k,ℓ)≠(2,2)) for which $$\begin{eqnarray}x(x+1)\cdots (x+k-1)=y^{\ell }.\end{eqnarray}$$ In particular, if we assume that ℓℓ is
Darmon, Erdős, Michael A. Bennett, Samir Siksek, Schinzel, Schoenfeld, Siksek   +6 more
core   +2 more sources

Equidistribution of signs for Hilbert modular forms of half-integral weight

, 2018
We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence.
Kaushik, Surjeet, Kumar, Narasimha, Tanabe, Naomi   +2 more
core   +1 more source

Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems [PDF]

, 2008
In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations.
Abraham R, Arnold V I, Bloch A, Claudia Wulff, Derks G, George W Patrick, Mark Roberts, Marsden J E, Meyer K R, Niederman L, van der Meer J-C, Weinstein A   +11 more
core   +3 more sources

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
doaj   +1 more source

On Borcherds products associated with lattices of prime discriminant

, 2003
We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions.
Bruinier, Jan H., Bundschuh, M.
core   +1 more source

Kodaira–Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace

Forum of Mathematics, Sigma
We consider integral models of Hilbert modular varieties with Iwahori level structure at primes over p, first proving a Kodaira–Spencer isomorphism that gives a concise description of their dualizing sheaves. We then analyze fibres of the degeneracy maps
Fred Diamond
doaj   +1 more source

L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Forum of Mathematics, Sigma
Let $\pi $ be a cuspidal, cohomological automorphic representation of an inner form G of $\operatorname {{PGL}}_2$ over a number field F of arbitrary signature. Further, let $\mathfrak {p}$ be a prime of F such that G is split at
Lennart Gehrmann, Maria Rosaria Pati
doaj   +1 more source

An explicit Waldspurger formula for Hilbert modular forms

, 2018
We describe a construction of preimages for the Shimura map on Hilbert modular forms, and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted L-functions.
Sirolli, Nicolás, Tornaría, Gonzalo
core   +1 more source

Nonvanishing of twists of $L$-functions attached to Hilbert modular forms

, 2014
We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and predictions ...
Ryan, Nathan C., Tornaria, Gonzalo, Voight, John   +2 more
core   +1 more source

Hecke operators on Hilbert-Siegel modular forms

, 2007
We define Hilbert-Siegel modular forms and Hecke "operators" acting on them. As with Hilbert modular forms, these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo ...
Caulk, Suzanne, Walling, Lynne H.
core   +1 more source