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math.NT2024
On the arithmetic inner product formula and central derivatives of L-functions
Tuoping Du
This research provides a formal definition of the arithmetic theta lift for cusp forms of weight and establishes the arithmetic inner product formula, thereby completing the…
math.NT2024
An exact way to verify whether n is a congruent number using Heegner points
Heng Chen, Rong Ma, Tuoping Du
We introduce the relationship between congruent numbers and elliptic curves, and compute the conductor of the elliptic curve associated with it. Furthermore, we…
math.NT2014
Ternary quadratic forms and Heegner divisors
Tuoping Du
In this paper, I use Siegel-Weil formula and Kudla matching principle to prove some interesting identities between representation number (of ternary quadratic space) and the degree…