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Displaying 41 – 60 of 242

Zeros of Fekete polynomials

Brian Conrey, Andrew Granville, Bjorn Poonen, K. Soundararajan (2000)

Annales de l'institut Fourier

For $p$ an odd prime, we show that the Fekete polynomial $f_{p} (t) = \sum_{a = 0}^{p - 1} (\frac{a}{p}) t^{a}$ has $\sim κ_{0} p$ zeros on the unit circle, where $0.500813 > κ_{0} > 0.500668$ . Here $κ_{0} - 1 / 2$ is the probability that the function $1 / x + 1 / (1 - x) + \sum_{n \in ℤ : n \neq 0, 1} δ_{n} / (x - n)$ has a zero in $] 0, 1 [$ , where each $δ_{n}$ is $\pm 1$ with y $1 / 2$ . In fact $f_{p} (t)$ has absolute value $\sqrt{p}$ at each primitive $p$ th root of unity, and we show that if $| f_{p} (e (2 i π (K + τ) / p)) | < ϵ \sqrt{p}$ for some $τ \in] 0, 1 [$ then there is a zero of $f$ close to this arc.

We show that in a cyclic group with $n$ elements every zero-sumfree sequence $S$ with length $| S | \geq \frac{n + 1}{2}$ contains some element of order $n$ with high multiplicity.

Currently displaying 41 – 60 of 242

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Displaying 41 – 60 of 242

Zeros of Fekete polynomials

Zeros of Hecke L-functions associated with cusp forms

Zeros of L-Functions Attached to Maass Forms.

Zeros of p-adic L-functions

Zeros of p-adic L-functions

Zeros of polynomials and exponential diophantine equations

Zeros of polynomials over valued fields.

Zeros of quadratic zeta-functions on the critical line

Zeros of smallest modulus of functions resembling exp(z).

Zeros of the constant term in the Chowla-Selberg formula

Zeros of the Riemann Zeta-function on the critical line.

Zeros on the Critical Line for Dirichlet Series Attached to Certain Cusp Forms.

Zeros on the critical line for Maass wave form L-functions.

Zero-sum bipartite Ramsey numbers

Zero-sumfree sequences in cyclic groups and some arithmetical application

Zero-sums of length kq in $ℤ_{q}^{d}$

Zeta function and Zharkovskaya's theorem on Siegel modular forms of half-integral weight

Zeta Functions and Composition Factors for Arithmetic Orders.

Zeta functions and counting finite $p$ -groups.

Zeta functions and Eichler integrals

Currently displaying 41 – 60 of 242