Homology of GL over infinite fields outside the stability range

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

Homology of Projective Space over Finite Fields

Sums of Twisted Gl(2) L-functions over Function Fields

Let K be a function field of odd characteristic, and let π (resp., η) be a cuspidal automorphic representation of GL2(AK ) (resp., GL1(AK )). Then we show that a weighted sum of the twists of L(s, π) by quadratic characters χD , ∑ D L(s, π ⊗ χD) a0(s, π, D) η(D) |D|, is a rational function and has a finite, nonabelian group of functional equations. A similar construction in the noncuspidal case...

Representations of GL(2) and SL(2) over finite fields

Irreducible complex representations of GL(2) and SL(2) over a finite field can be classified by methods useful for p-adic reductive groups and real Lie groups. (See Piatetski-Shapiro’s inspiring A.M.S. Memoir on this subject.) That is, we first see that most principal series representations are irreducible. We determine the irreducible constituents of the irregular principal series. We prove th...

On Computing Homology Gradients over Finite Fields

Recently the so-called Atiyah conjecture about l-Betti numbers has been disproved. The counterexamples were found using a specific method of computing the spectral measure of a matrix over a complex group ring. We show that in many situations the same method allows to compute homology gradients, i.e. generalizations of l-Betti numbers to fields of arbitrary characteristic. As an application we ...