Gaussian Primes in Narrow Sectors

Joshua Stucky

Type: Article

Publication Date: 2021-01-28

Citations: 1

DOI: https://doi.org/10.1093/qmath/haab009

Abstract

Abstract We generalize a Theorem of Ricci and count Gaussian primes $\mathfrak{p}$ with short interval restrictions on both the norm and the argument of $\mathfrak{p}$. We follow Heath-Brown’s method for counting rational primes in short intervals.

Locations

arXiv (Cornell University) - View - PDF
The Quarterly Journal of Mathematics - View

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Works Cited by This (12)

Action	Title	Year	Authors
+	A Brun-Titschmarsh theorem for multiplicative functions.	1980	Peter Shiu
+	On the difference between consecutive primes	1971	M. N. Huxley
+	A zero‐free region for the Hecke <i>L</i> ‐functions	1990	Mark D. Coleman
+	On the distance between consecutive prime ideal numbers in sectors	1983	M. Maknys
+	The Distribution of Points at which Binary Quadratic Forms are Prime	1990	Mark D. Coleman
+	Zeros of Hecke Z-functions and the distribution of primes of an imaginary quadratic field	1976	M. Maknys
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown
+	On the Hecke Z-functions of an imaginary quadratic field	1976	M. Maknys
+ PDF Chat	Prime Numbers in Short Intervals and a Generalized Vaughan Identity	1982	D. R. Heath‐Brown
+	Local Distribution Of Primes.	1976	Stephen John Ricci