We show that the percentage of primitive forms level one and weight $4k\rightarrow \infty$ for which associated $L$-function at central point is no less than $(\log{k})^{-2}$ least 20%. The key ingredients our proof are Kuznetsov convolution formula Liouville-Green method.

In this work, the ionic liquid triethylamine-bonded sulfonic acid {[Et3N–SO3H]Cl}, N,N-diethyl-N-sulfoethanammonium chloride was used as a green acidic homogeneous catalyst to synthesis of 3,4-dihydropyrimidin-2(1H)-ones and 3,4-dihydropyrimidin-2(1H)-thiones as two categories of heterocycles, from aldehyde, dicarbonyl compound and urea or thiourea throughout the one-pot three components cycloc...

nowadays, paying attention to the environmental needs and desires of consumersand trying to satisfy them by designing marketing activities in an environmentallyfriendly way, is the best way to increase their satisfaction and finally, gaincompetitive advantage. prior research has paid much attention to the consumerbehavior and marketing activities of corporate organizations, but none has studied...