Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Halupczok, Karin"'
Autor:
Halupczok, Karin, Ohst, Marvin
We prove that for all constants $a\in\N$, $b\in\Z$, $c,d\in\R$, $c\neq 0$, the fractions $\phi(an+b)/(cn+d)$ lie dense in the interval $]0,D]$ (respectively $[D,0[$ if $c<0$), where $D=a\phi(\gcd(a,b))/(c\gcd(a,b))$. This interval is the largest poss
Externí odkaz:
http://arxiv.org/abs/2411.11065
Autor:
Halupczok, Karin, Munsch, Marc
We prove large sieve inequalities with multivariate polynomial moduli and deduce a general Bombieri--Vinogradov type theorem for a class of polynomial moduli having a sufficient number of variables compared to its degree. This sharpens previous resul
Externí odkaz:
http://arxiv.org/abs/2110.13257
Autor:
Bhowmik, Gautami, Halupczok, Karin
We present an overview of bounds on zeros of $L$-functions and obtain some improvements under weak conjectures related to the Goldbach problem.
Comment: To appear in Combinatorial and Additive Number Theory IV, Springer
Comment: To appear in Combinatorial and Additive Number Theory IV, Springer
Externí odkaz:
http://arxiv.org/abs/2010.01308
Autor:
Bhowmik, Gautami, Halupczok, Karin
We present a historical account of the asymptotics of classical Goldbach representations with special reference to the equivalence with the Riemann Hypothesis. When the primes are chosen from an arithmetic progression comparable but weaker relationsh
Externí odkaz:
http://arxiv.org/abs/1809.06920
Autor:
Halupczok, Karin
We prove two bounds for discrete moments of Weyl sums. The first one can be obtained using a standard approach. The second one involves an observation how this method can be improved, which leads to a sharper bound in certain ranges. The proofs both
Externí odkaz:
http://arxiv.org/abs/1804.05587
Publikováno v:
Mathematika 65 (2019) 57-97
Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression. On the other hand the existence of good error terms
Externí odkaz:
http://arxiv.org/abs/1704.06103
Autor:
Halupczok, Karin
We prove a version of the Bombieri--Vinogradov Theorem with certain products of Gaussian primes as moduli, making use of their special form as polynomial expressions in several variables. Adapting Vaughan's proof of the classical Bombieri--Vinogadov
Externí odkaz:
http://arxiv.org/abs/1607.07265
Autor:
Halupczok, Karin
Some mean value theorems in the style of Bombieri-Vinogradov's theorem are discussed. They concern binary and ternary additive problems with primes in arithmetic progressions and short intervals. Nontrivial estimates for some of these mean values are
Externí odkaz:
http://arxiv.org/abs/1212.4406
Autor:
Halupczok, Karin, Suger, Benjamin
We consider Mertens' function M(x,q,a) in arithmetic progression, Assuming the generalized Riemann hypothesis (GRH), we show an upper bound that is uniform for all moduli which are not too large. For the proof, a former method of K. Soundararajan is
Externí odkaz:
http://arxiv.org/abs/1111.3305
Autor:
Halupczok, Karin
We give a new bound for the large sieve inequality with power moduli q^k that is uniform in k. The proof uses a new theorem due to T. Wooley from his work on efficient congruencing.
Comment: 9 pages; accepted by IJNT
Comment: 9 pages; accepted by IJNT
Externí odkaz:
http://arxiv.org/abs/1109.3975