scholarly journals Sign changes of Kloosterman sums and exceptional characters

2018 ◽  
Vol 147 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Sary Drappeau ◽  
James Maynard
Keyword(s):  
Kloosterman Sums ◽  
Sign Changes

scholarly journals Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum

2020 ◽  
Author(s):  
Ping Xi
Keyword(s):  
Kloosterman Sums ◽  
Kloosterman Sum ◽  
Sign Changes ◽  
Prime Factors ◽  
Quantitative Statement ◽  
Almost Prime

Abstract We give a corrigendum to the previous paper [ 8] and recover the same quantitative statement: the Kloosterman sum changes sign infinitely often as the modulus runs over squarefree numbers with at most seven prime factors.

scholarly journals Sign changes in the prime number theorem

2021 ◽  
Author(s):  
Thomas Morrill ◽  
Dave Platt ◽  
Tim Trudgian
Keyword(s):  
Prime Number ◽  
Prime Number Theorem ◽  
Sign Changes

scholarly journals Ordering risk bounds in factor models

2018 ◽  
Vol 6 (1) ◽  
pp. 259-287 ◽  
Author(s):  
Jonathan Ansari ◽  
Ludger Rüschendorf
Keyword(s):  
Risk Factor ◽  
Systemic Risk ◽  
Factor Models ◽  
Worst Case ◽  
Sign Changes ◽  
Risk Factor Models ◽  
Risk Bounds ◽  
Derivatives Of ◽  
Dependence Structures

AbstractConditionally comonotonic risk vectors have been proved in [4] to yield worst case dependence structures maximizing the risk of the portfolio sum in partially specified risk factor models. In this paper we investigate the question how risk bounds depend on the specification of the pairwise copulas of the risk components Xiwith the systemic risk factor. As basic toolwe introduce a new ordering based on sign changes of the derivatives of copulas. This together with discretization by n-grids and the theory of supermodular transfers allows us to derive concrete ordering criteria for the maximal risks.

Estimates for Kloosterman sums for totally real number fields

2001 ◽  
Vol 2001 (535) ◽  
Author(s):  
R. W. Bruggeman ◽  
R. J. Miatello ◽  
I. Pacharoni
Keyword(s):  
Real Number ◽  
Number Fields ◽  
Kloosterman Sums ◽  
Totally Real

ON THE GENERAL k-TH KLOOSTERMAN SUMS AND ITS FOURTH POWER MEAN

2004 ◽  
Vol 25 (01) ◽  
pp. 97-102 ◽  
Author(s):  
HONGYAN LIU ◽  
WENPENG ZHANG
Keyword(s):  
Kloosterman Sums ◽  
Fourth Power ◽  
Power Mean ◽  
Fourth Power Mean

scholarly journals Short Kloosterman Sums for Polynomials over Finite Fields

2003 ◽  
Vol 55 (2) ◽  
pp. 225-246 ◽  
Author(s):  
William D. Banks ◽  
Asma Harcharras ◽  
Igor E. Shparlinski
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Small Degree ◽  
Kloosterman Sums ◽  
Degree Relative ◽  
Irreducible Polynomials ◽  
Arbitrary Polynomial ◽  
Polynomials Over Finite Fields ◽  
Titchmarsh Theorem

AbstractWe extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring [x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.

scholarly journals On the number of sign changes in the remainder-term of the prime-ideal theorem

1988 ◽  
Vol 56 (1) ◽  
pp. 185-197 ◽  
Author(s):  
J. Kaczorowski ◽  
W. Staś
Keyword(s):  
Prime Ideal ◽  
Remainder Term ◽  
Sign Changes ◽  
Prime Ideal Theorem
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