On the smallest pseudopower
On the sphere problem.
One of the oldest problems in analytic number theory consists of counting points with integer coordinates in the d-dimensional ball. It is very easy to find a main term for the counting function, but the size of the error term is difficult to estimate (...).
On the sums
On the torsion of the Jacobians of the hyperelliptic curves y² = xⁿ + a and y² = x(xⁿ+a)
Consider two families of hyperelliptic curves (over ℚ), and , and their respective Jacobians , . We give a partial characterization of the torsion part of and . More precisely, we show that the only prime factors of the orders of such groups are 2 and prime divisors of n (we also give upper bounds for the exponents). Moreover, we give a complete description of the torsion part of . Namely, we show that . In addition, we characterize the torsion parts of , where p is an odd prime, and...
On the Vinogradov bound in the three primes Goldbach conjecture
On the zeta function of monodromy of a polynomial map
On Transformation of Exceptional sets
On twisted exponential sums.
On two problems of Mordell about exponential sums
On Vinogradov's estimate of trigonometric sums and the Goldbach-Vinogradov theorem
On Waldspurger's theorem
On Zeros of Dirirchlet's L Series.
Optimal bounds for exponential sums in terms of discrepancy
Oscillations of Hecke eigenvalues at shifted primes.
In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments.