Tate conjecture for twisted Siegel modular threefolds
The arithmetic of function fields
The Bloch-Wigner-Ramakrishnan polylogarithm function.
The Chowla-Selberg formula for genera
The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer
The class number one problem for the non-abelian normal CM-fields of degree 16
The class number one problem for the non-normal sextic CM-fields. Part 2
The class number one problem for the real quadratic fields ℚ(√((an)²+4a))
We solve unconditionally the class number one problem for the 2-parameter family of real quadratic fields ℚ(√d) with square-free discriminant d = (an)²+4a for positive odd integers a and n.
The complete determination of wide Richaud-Degert types which are not 5 modulo 8 with class number one
The derivative of p-adic L-functions
The distribution of zeros of Epstein zeta functions over GLₙ
The Fourier expansion of Epstein's zeta function for totally real algebraic number fields and some consequences for Dedekind's zeta function
The Fourier expansion of Epstein's zeta function over an algebraic number field and its consequences for algebraic number theory
The Galois module structure of algebraic integer rings in fields with generalised quaternion group
The growth rate of the Dedekind Zeta-function on the critical line
The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic sextic fields with class numbers equal to their genus class numbers.
The least prime which does not split completely.
The multiplicative and functional independence of Dedekind zeta functions of abelian fields
It is shown that the multiplicative independence of Dedekind zeta functions of abelian fields is equivalent to their functional independence. We also give all the possible multiplicative dependence relations for any set of Dedekind zeta functions of abelian fields.
The Normal Density of Prime Ideals in Small Regions.
The refined p-adic abelian Stark conjecture in function fields.