Let $$\phi $$ be an even Hecke–Maass cusp form on $${{\text {SL}}}_2({\mathbb {Z}})$$ whose L-function does not vanish at the center of functional equation. In this article, we obtain exact formula average triple products , f and $${\bar{f}}$$ where runs over orthonormal basis $$H_k$$ Hecke eigen elliptic forms a fixed weight $$k\geqslant 4$$ . As application, prove quantitative non-vanishing r...

A description and an example are given of numerical experiments which look for a relation between modular forms for certain congruence subgroups of SL(3, ZZ) and Galois representations.

Background: The aim of this study was to investigate the effect of the electromagnetic field (EMF) generated by 10 kV (50 Hz) high voltage line on the epididymal sperm characteristics and the protective effects of ganoderma lucidum (GL) and melatonin (M) in EMF exposed male rats. Materials and Methods: In this study, 64 Wistar rats were divided into 8 groups (n= 8). Rats in 26-day and 52-day ex...

background & aim: lemon verbena (lippia citriodora h.b.k.) is a richly scented herb and has a long history as a sacred and medicinal plant. select an appropriate medium in tissue culture is a necessity for success experimental: to evaluate the effect of 10 medium of previous researches for lippia micropropagation (1- ms medium supplemented with bap (3 mgl-1) + iba (0.1 mgl-1) + activated ch...

PURPOSE Although previous research has associated the glycaemic load (GL) of a meal with cognitive functioning, typically the macro-nutrient composition of the meals has differed, raising a question as to whether the response was to GL or to the energy, nutrients or particular foods consumed. Therefore, the present study contrasted two breakfasts that offered identical levels of energy and macr...

We refute a recent claim in the literature of a " new " quantum deformation of GL(2). Until the year 2000 it was not clear how many distinct quantum group deformations are admissible for the group GL(2) and the supergroup GL(1|1). For the group GL(2) there were the well-known standard GL pq (2) [1] and nonstandard (Jordanian) GL gh (2) [2] two-parameter deformations. (The dual quantum algebras ...

for the error term in Gauss’ classical circle problem, improving greatly on Gauss’ own bound O(x1/2). Though Voronoi originally deduced his formulas from Poisson summation in R2, applied to appropriately chosen test functions, one nowadays views his formulas as identities involving the Fourier coefficients of modular forms on GL(2), i.e., modular forms on the complex upper half plane. A discuss...

Signal transducer and activator of transcription (STAT)-3 inhibitors play an important role in regulating immune responses. Galiellalactone (GL) is a fungal secondary metabolite known to interfere with the binding of phosphorylated signal transducer and activator of transcription (pSTAT)-3 as well of pSTAT-6 dimers to their target DNA in vitro. Intra nasal delivery of 50 μg GL into the lung of ...

3D (3 dimensional) Young diagrams are a generalization of 2D diagrams. In this paper, We consider Bosons and 3-Jack polynomials. associate three parameters $h_1,h_2,h_3$ to $y,x,z$-axis respectively. polynomials $P_{n,j}, n\geq j$ with coefficients in $\mathbb C(h_1,h_2,h_3)$, which the Schur functions Jack case. Similar functions, can also be determined by vertex operators Pieri formulas.

The Iwahori-Hecke algebra Hk(q ) of type A acts on tensor product space V ⊗k of the natural representation of the quantum superalgebra Uq(gl(m, n)). We show this action of Hk(q ) and the action of Uq(gl(m, n)) on the same space determine commuting actions of each other. Together with this result and Gyoja’s q-analogue of the Young symmetrizer, we construct a highest weight vector of each irredu...