On explicit estimates for S(t), S1(t), and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>?</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:math> under the Riemann Hypothesis
نویسندگان
چکیده
Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $\zeta\left(1/2+\mathrm{i}t\right)$ while comparing them with recently proven unconditional ones. As a corollary obtain conditional bound on gaps between consecutive zeros zeta-function.
منابع مشابه
the effect of explicit teaching of metacognitive vocabulary learning strategies on recall and retention of idioms
چکیده ندارد.
15 صفحه اولOn the Riemann Hypothesis for function fields
We prove a variant of Connes’s trace formula and show how it can be used to give a new proof of the Riemann hypothesis for L-functions with Größencharacter for function fields.
متن کاملOn Robin’s criterion for the Riemann Hypothesis
Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality σ(n) := ∑ d|n d < en log log n is satisfied for n ≥ 5041, where γ denotes the Euler(Mascheroni) constant. We show by elementary methods that if n ≥ 37 does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreo...
متن کاملComment on the Riemann Hypothesis
The Riemann hypothesis is identified with zeros of N = 4 supersymmetric gauge theory four-point amplitude. The zeros of the ζ(s) function are identified with th complex dimension of the spacetime, or the dimension of the toroidal compactification. A sequence of dimensions are identified in order to map the zeros of the amplitude to the Riemann hypothesis.
متن کاملThe Riemann Hypothesis
Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann’s zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis. For simplicity, G here denotes a classical semi-simple algebraic group defined over the field Q of rationals. With a fixed Borel, as usual, ∆0 stands...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2022
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2021.05.014