Under two assumptions, we determine the distribution of the difference between two functions each counting the numbers x that are in a given arithmetic progression modulo q and the...
In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f S2k(N) satisfying certain conditions, we c...
We give an example of a noncongruence subgroup Γ ⊂ SL(2, Z) whose space of weight 3 cusp forms S3(Γ) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations wi...
Liqun Fang, J. William Hoffman, Benjamin Linowitz,...
For diagonal cubic surfaces, we study the behaviour of the height of the smallest rational point versus the Tamagawa type number introduced by E. Peyre.