On Grosswald's conjecture on primitive roots
Grosswald’s conjecture is that g(p), the least primitive root modulo p, satisfies g(p) ≤ √p - 2 for all p > 409. We make progress towards this conjecture by proving that g(p) ≤ √p -2 for all and for all .
On Groups of Squarefree Order.
On Grunwald-Wang's theorem.
On guessing whether a sequence has a certain property.
On Hall's conjecture
On happy factorizations.
On h-bases for n.
On h-bases for n II.
On Hecke eigenforms of half-integral weight.
On Hecke eigenvalues at primes of the form [g(n)]
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].
On Hecke -functions associated with cusp forms. II: On the sign changes of .
On Hecke L-functions associated with cusp forms
On heights of multiplicatively dependent algebraic numbers
On Heron triangles.
On higher moments of Hecke eigenvalues attached to cusp forms
Let , and be three distinct primitive holomorphic cusp forms of even integral weights , and for the full modular group , respectively, and let , and denote the th normalized Fourier coefficients of , and , respectively. We consider the cancellations of sums related to arithmetic functions , twisted by and establish the following results: for any , where , are any fixed positive integers.
On higher-power moments of E(t)
On higher-power moments of Δ(x)
On higher-power moments of Δ(x) (II)
On higher-power moments of Δ(x) (III)
On Hilbert modular forms modulo p: explicit ring structure.
H. P. F. Swinnerton-Dyer determined the structure of the ring of modular forms modulo p in the elliptic modular case. In this paper, the structure of the ring of Hilbert modular forms modulo p is studied. In the case where the discriminant of corresponding quadratic field is 8 (or 5), the explicit structure is determined.