Mathematics > Number Theory
[Submitted on 11 Oct 2025
]
Title: $L$-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings
Title: $L$- 通过正则化θ提升在实二次域的环类扩张中椭圆曲线的函数
Abstract: We derive new integral presentations for central derivative values of $L$-functions of elliptic curves defined over the rationals, basechanged to a real quadratic field $K$, twisted by ring class characters of $K$ in terms of sums along ``geodesics" corresponding to the class group of $K$ of automorphic Green's functions for certain Hirzebruch-Zagier-like arithmetic divisors on Hilbert modular surfaces. We also relate these sums to Birch-Swinnerton-Dyer constants and periods.
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