In this paper, we study the moments of central values certain unitary families Hecke L-functions Gaussian field, and establish quantitative non-vanishing result for their values. We also a one level density low-lying zeros these L-functions.

Given a nilpotent Lie algebra L of dimension $$\le 6$$ on an arbitrary field characteristic $$\ne 2$$ , we show direct method to detect whether is capable or not via computations the size its nonabelian exterior square $$L \wedge L$$ . For dimensions higher than 6, result general nature, based evidences low dimensional case, but also large families algebras, namely generalized Heisenberg algebr...

We provide comparison results for anticyclotomic [Formula: see text]-adic text]-functions attached to Hida families of modular forms. The main result is a between the restriction three variable text]-function introduced by Skinner and Urban, constructed means Gross points in setting definite quaternion algebras. Several auxiliary involving Chida-Hsieh Büyükboduk–Lei are also proved.

Let fnew be a classical newform of weight ≥2 and prime to p level. We study the arithmetic its unique p-stabilisation f when is p-irregular, that is, Hecke polynomial at admits single repeated root. In particular, we p-adic families through base-change an imaginary quadratic field F where splits, prove respective eigencurves are both Gorenstein f. use this construct two-variable L-function over...