An L-function free proof of Hua's Theorem on sums of five prime squares

Claus Bauer

doi:10.1556/012.2020.57.1.1456

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 1

An L-function free proof of Hua's Theorem on sums of five prime squares

Author:

Claus Bauer

Claus Bauer Dolby Laboratories

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Pages:: 1–39

Online Publication Date:: Mar 2020

Publication Date:: 01 Mar 2020

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/012.2020.57.1.1456

Keywords:: Primary 11 (P32); 11 (P70); 11 (N35); Additive questions involving primes; sieves

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Abstract

We provide a new proof of Hua's result that every sufficiently large integer N ≡ 5 (mod 24) can be written as the sum of the five prime squares. Hua's original proof relies on the circle method and uses results from the theory of L-functions. Here, we present a proof based on the transference principle first introduced in[5]. Using a sieve theoretic approach similar to ([10]), we do not require any results related to the distributions of zeros of L- functions. The main technical difficulty of our approach lies in proving the pseudo-randomness of the majorant of the characteristic function of the W-tricked primes which requires a precise evaluation of the occurring Gaussian sums and Jacobi symbols.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language	English French German
Size	B5
Year of Foundation	1966
Volumes per Year	1
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ISSN	0081-6906 (Print)
ISSN	1588-2896 (Online)