skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Brüdern, Jörg"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, International Mathematics Research Notices)
    We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $$k$$ delivering essentially optimal bounds for moments of order $$u$$ whenever $$u>2\lfloor k/2\rfloor +4$$. 
    more » « less
    Free, publicly-accessible full text available November 26, 2025
  2. ; (, Journal of the European Mathematical Society)
    Let $$k$$ be a natural number and let $$c=2.134693\ldots$$ be the unique real solution of the equation $$2c=2+\log (5c-1)$$ in $$[1,\infty)$$. Then, when $$s\ge ck+4$$, we establish an asymptotic lower bound of the expected order of magnitude for the number of representations of a large positive integer as the sum of one prime and $$s$$ positive integral $$k$$-th powers. 
    more » « less
    Free, publicly-accessible full text available November 28, 2025
  3. ; (, Functiones et Approximatio Commentarii Mathematici)
    Full Text Available 
  4. ; (, Bulletin of the London Mathematical Society)
    We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of . In particular, when and is defined via the relation , then for all large numbers there is an integer with for which . 
    more » « less
    Free, publicly-accessible full text available March 1, 2026
  5. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Let G ⁢ ( k ) {G(k)}denote the least numbershaving the property that everysufficiently large natural number is the sum of at mostspositive integralk-th powers.Then for all k ∈ ℕ {k\in\mathbb{N}}, one has G ⁢ ( k ) ⩽ ⌈ k ⁢ ( log ⁡ k + 4.20032 ) ⌉ . G(k)\leqslant\lceil k(\log k+4.20032)\rceil. Our new methods improve on all bounds available hitherto when k ⩾ 14 {k\geqslant 14}. 
    more » « less
    Full Text Available 
  6. ; (, International Mathematics Research Notices)
    Abstract We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in $26$ or more variables. In certain cases, pairs in $25$ variables can be handled. 
    more » « less
    Full Text Available 
  7. ; (, Journal of the London Mathematical Society)
    Abstract Let satisfy . Freĭman's theorem shows that when , there exists such that all large integers are represented in the form , with , if and only if diverges. We make this theorem effective by showing that, for each fixed , it suffices to impose the conditionMore is established when the sequence of exponents forms an arithmetic progression. Thus, for example, when and , all large integers are represented in the form , with . 
    more » « less
  8. ; (, The Quarterly Journal of Mathematics)
    Abstract We establish the non-singular Hasse principle for pairs of diagonal quartic equations in 22 or more variables. 
    more » « less
  9. ; (, Bulletin of the London Mathematical Society)
    We consider certain systems of three linked simultaneous diagonal equations in ten variables with total degree exceeding five. By means of a complification argument, we obtain an asymptotic formula for the number of integral solutions of this system of bounded height that resolves the associated paucity problem. 
    more » « less
    Full Text Available 
  10. ; (, Acta Arithmetica)
    Full Text Available