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Universal murmuration and Hecke augmentation
Shenghao Hua, Chung Pang Mok
Prime coefficients of elliptic curves exhibit murmurations, statistical patterns that support the prediction of arithmetic labels. We conjecture that root number weighted averages…
On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator
Ziran Liu, Chung Pang Mok
This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational cas…
On the Birch and Swinnerton-Dyer formula modulo squares for certain quadratic twists of elliptic curves
Alexander J. Barrios, Chung Pang Mok
Let be an elliptic curve with conductor , where and are coprime and is squarefree. Let be a positive fundamental discriminant satisfy…
On a theorem of Bertolini-Darmon about rationality of Stark-Heegner points over genus fields of real quadratic fields
Chung Pang Mok
In this paper, we remove certain hypothesis in the theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over narrow genus class fields of real quadratic fields. A…