scholarly journals On the real zeros of random trigonometric polynomials with dependent coefficients

2018 ◽  
Vol 147 (1) ◽  
pp. 205-214
Author(s):  
Jürgen Angst ◽  
Federico Dalmao ◽  
Guillaume Poly
Keyword(s):  
Trigonometric Polynomials ◽  
The Real ◽  
Real Zeros

scholarly journals On a partial theta function and its spectrum

2016 ◽  
Vol 146 (3) ◽  
pp. 609-623 ◽  
Author(s):  
Vladimir Petrov Kostov
Keyword(s):  
Entire Function ◽  
Theta Function ◽  
Local Minimum ◽  
Real Zero ◽  
Positive Real ◽  
The Real ◽  
Real Zeros ◽  
Partial Theta Function

The bivariate series defines a partial theta function. For fixed q (∣q∣ < 1), θ(q, ·) is an entire function. For q ∈ (–1, 0) the function θ(q, ·) has infinitely many negative and infinitely many positive real zeros. There exists a sequence of values of q tending to –1+ such that has a double real zero (the rest of its real zeros being simple). For k odd (respectively, k even) has a local minimum (respectively, maximum) at , and is the rightmost of the real negative zeros of (respectively, for k sufficiently large is the second from the left of the real negative zeros of ). For k sufficiently large one has . One has and .

On the real zeros of the function ζ(1/2 +it)

1985 ◽  
Vol 40 (4) ◽  
pp. 191-192
Author(s):  
A A Karatsuba
Keyword(s):  
The Real ◽  
Real Zeros

The average number of real zeros of a random trigonometric polynomial

1968 ◽  
Vol 64 (3) ◽  
pp. 721-730 ◽  
Author(s):  
Minaketan Das
Keyword(s):  
Trigonometric Polynomial ◽  
Mathematical Expectation ◽  
Random Variables ◽  
Trigonometric Polynomials ◽  
Real Zeros ◽  
Number Of Zeros ◽  
Number Of Real Zeros ◽  
Random Trigonometric Polynomial ◽  
Image Position ◽  
Mutually Independent

AbstractLet a1, a2,… be a sequence of mutually independent, normally distributed, random variables with mathematical expectation zero and variance unity; let b1, b2,… be a set of positive constants. In this work, we obtain the average number of zeros in the interval (0, 2π) of trigonometric polynomials of the formfor large n. The case when bk = kσ (σ > − 3/2;) is studied in detail. Here the required average is (2σ + 1/2σ + 3)½.2n + o(n) for σ ≥ − ½ and of order n3/2; + σ in the remaining cases.

The Real Zeros of Struve’s Function

1970 ◽  
Vol 1 (3) ◽  
pp. 365-375 ◽  
Author(s):  
J. Steinig
Keyword(s):  
The Real ◽  
Real Zeros

The real zeros of the confluent hypergeometric function

1956 ◽  
Vol 52 (4) ◽  
pp. 626-635 ◽  
Author(s):  
L. J. Slater
Keyword(s):  
Hypergeometric Function ◽  
Numerical Evaluation ◽  
Confluent Hypergeometric Function ◽  
The Real ◽  
Real Zeros ◽  
Image Position

This paper contains a discussion of various points which arise in the numerical evaluation of the small real zeros of the confluent hypergeometric functionwhereThere are two distinct problems, first the determination of those values of x for which M(a, b; x) = 0, given a and b, and secondly the study of the curves represented by M (a, b; x) = 0, for fixed values of x. These curves all lie on the surface M(a, b; x) = 0, of course.

On the real zeros of trigonometrical polynomials

1973 ◽  
Vol 26 (1) ◽  
pp. 235-242
Author(s):  
Zalman Rubinstein
Keyword(s):  
The Real ◽  
Real Zeros
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