A Riemann-Hurwitz formula for the Selmer group of an elliptic curve with complex multiplication.
A rigidity phenomenon for the Hardy-Littlewood maximal function
The Hardy-Littlewood maximal function ℳ and the trigonometric function sin x are two central objects in harmonic analysis. We prove that ℳ characterizes sin x in the following way: Let be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator has a critical point at r = γ for every x ∈ ℝ, then f(x) = a + bsin(cx+d) for some a,b,c,d ∈ ℝ. This statement can be used to derive a characterization of trigonometric functions as those nonconstant...
A scattering theory for automorphic functions
A Schinzel theorem on continued fractions in function fields
A search for high rank congruent number elliptic curves.
A search for Tribonacci-Wieferich primes
Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present. This paper is devoted to a similar problem related to the Tribonacci numbers.
A self-indexed sequence.
A self-similar tiling generated by the minimal Pisot number
A sequence adapted from the movement of the center of mass of two planets in solar system
In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
A Sequence Has Almost Nowhere Small Discrepancy.
A sequence of binomial coefficients related to Lucas and Fibonacci numbers.
A Sequence of Exponential Numbers
A sequential Riesz-like criterion for the Riemann Hypothesis.
A series transformation formula and related polynomials.
A set of infinite measure whose ratio set does not contain a given sequence.
A set of squares without arithmetic progressions
A sextuple product identity with applications.
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
A sharp estimate of the number of integral points in a tetrahedron.
A sharpening of the bounds for linear forms in logarithms