ترغب بنشر مسار تعليمي؟ اضغط هنا

Even universal binary Hermitian lattices over imaginary quadratic fields

378   0   0.0 ( 0 )
 نشر من قبل Ji Young Kim Dr.
 تاريخ النشر 2009
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

A positive definite even Hermitian lattice is called emph{even universal} if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields $Q{-m}$ for all positive square-free integers $m$ and we list optimal criterions on even universality of Hermitian lattices over $Q{-m}$ which admits even universal binary Hermitian lattices.



قيم البحث

اقرأ أيضاً

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over $mathbb{Q}(sqrt{-m})$ for all m. For each imaginary quadratic field $mathbb{Q}(sqrt{-m})$, we obtain a criterion on universality of Hermitian latt ices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13,14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneebergers fifteen theorem and ours is the number 13.
We study the arithmetic of degree $N-1$ Eisenstein cohomology classes for locally symmetric spaces associated to $mathrm{GL}_N$ over an imaginary quadratic field $k$. Under natural conditions we evaluate these classes on $(N-1)$-cycles associated to degree $N$ extensions $F/k$ as linear combinations of generalised Dedekind sums. As a consequence we prove a remarkable conjecture of Sczech and Colmez expressing critical values of $L$-functions attached to Hecke characters of $F$ as polynomials in Kronecker--Eisenstein series evaluated at torsion points on elliptic curves with multiplication by $k$. We recover in particular the algebraicity of these critical values.
We prove Manins conjecture for four singular quartic del Pezzo surfaces over imaginary quadratic number fields, using the universal torsor method.
We give an explicit construct of a harmonic weak Maass form $F_{Theta}$ that is a lift of $Theta^3$, where $Theta$ is the classical Jacobi theta function. Just as the Fourier coefficients of $Theta^3$ are related to class numbers of imaginary quadrat ic fields, the Fourier coefficients of the holomorphic part of $F_{Theta}$ are associated to class numbers of real quadratic fields.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا