where ep(·) is the additive character ep(·) = e2πi·/p on the finite field Zp. For χ = χ0, the principal character, the sum is just a pure exponential sum S(χ0, f) = ∑p−1 x=1 ep(f(x)). Of course S(χ, f) = 0 unless χ(p−1)/d = χ0 where d = (k1, ..., kr, p− 1), as is easily seen from the change of variables x → xu if there is a u with u = 1 and χ(u) 6= 1. The classical Weil bound [12] (see [2] or [...

It is known that if x is a real residue character modulo k with x(p) = — 1 k n for the first five primes p, then the corresponding Fekete polynomial £„=j X(n)x changes sign on (0, 1). In this paper it is shown that the condition that x(p) be — 1 for the first four primes p is not sufficient to guarantee such a sign change. More specifically, if x ¡s the real nonprincipal character modulo either...

abounovas is of unique character who has  always stimulates old and new critics to battle against each other as far as each person makes a character for him based on their understanding and special orientation instead of discovering his true  character. to recognize his real character ,however, his biography must be reread and to have a correct and real conclusion we have to refer to  reliable ...

Proposition 4.1 (1) of this article is not correct as stated. For instance, if ε is the quadratic Dirichlet character of conductor 15, then there are two newforms in Sk(Γ1(15), ε) with coefficients in Q, and these are twists of each other by the quadratic character of conductor 3, whereas the quantity u in the proposition is 0 here. I am grateful to Steve Donnelly for pointing out this example....

Let (X, H) be a polarized, smooth, complex projective surface, and let v be a Chern character on X with positive rank and sufficiently large discriminant. In this paper, we compute the Gieseker wall for v in a slice of the stability manifold of X. We construct explicit curves parameterizing non-isomorphic Gieseker stable sheaves of character v that become S-equivalent along the wall. As a corol...

Let p be a prime, Zp the ring of p-adic integers, Qp the field of p-adic numbers, and Qp the algebraic closure of Qp. Let Fp be the algebraic closure of the finite field Fp, and ω : Fp → Qp the Techmüller lifting. Let q = pa, χ a multiplicative character of Fq into Q, and ψ a character of Zp[μq−1] into Q of exact order pn > 1, where μr is the set of r-th roots of unity in Qp. For simplicity, we...

The following is a quick set of notes of some properties of Dirichlet characters, in particular, how they are used to prove the infinitude of primes in arithmetic progressions. These notes are from from An Invitation to Modern Number Theory, by myself and Ramin Takloo-Bighash. As this is a modified snippet from the book, references to other parts of the book are displayed as ??. 1. Dirichlet Ch...

conclusions low onset age of smoking cigarettes, high novelty seeking and low cooperativeness in opiate dependents are among the important personality traits in future use of drugs that can predict the subsequent onset of using opiate drugs. results opiate addicts had higher scores in novelty seeking dimension and lower scores in cooperativeness compared to nicotine addicts. the onset age of sm...