In this paper we bound character sums of the shape ∑ n≤N χ 1 f n χ 2 f n+l , ; where χ1 and χ2 are non-principal multiplicative characters modulo a prime p, f(x) is a real-valued, twice-differentiable ...

Let p be an odd prime. Define $e_{n}=\cases (-1)^{n+\overline{n}}, & \text{if}\ n\ \text{is a quadratic residue mod}\ p\,\\ (-1)^{n+\overline{n}+1}, & \text{if}\ n ...

Number sequences are sets of numbers that follow a pattern or a rule. Each number in a sequence is called a term. A sequence which increases or decreases by the same amount each time is called a ...

CERTAIN quadratic series abound in prime numbers 1. Take, for example, the following Sequence in which the consecutive differences are 2, 4, 6, 8, etc. These are all prime numbers; the next term in ...