Zobrazeno 1 - 10
of 296
pro vyhledávání: '"11m99"'
Autor:
Lodone, Giovanni
We try to approach a known equivalence to RH involving relative maxima and minima of Xi(t) on critical line by a representation of the derivative of the phase of Xi(s) with respect to imaginary coordinate that involves directly Euler product. In this
Externí odkaz:
http://arxiv.org/abs/2412.11130
Autor:
Lodone, Giovanni
We try to apply a known equivalence, for RH about Riemann Z function, to Dirichlet L functions with primitive characters. The aim is to give a small contribution to the proof of the generalized version of Riemann Hypothesis (RH).
Comment: 21 pag
Comment: 21 pag
Externí odkaz:
http://arxiv.org/abs/2412.00169
Autor:
Matsumoto, Kohji, Suzuki, Masatoshi
We study the $M$-functions, which describe the limit theorem for the value-distributions of the secondary main terms in the asymptotic formulas for the summatory functions of the Goldbach counting function. One of the new aspects is a sufficient cond
Externí odkaz:
http://arxiv.org/abs/2409.00888
Autor:
Djanković, Goran, Khan, Rizwanur
We obtain an asymptotic for the fourth moment of truncated Eisenstein series of large Laplacian eigenvalue, verifying for the first time that the main term corresponds to Gaussian random behavior. This is a manifestation of the Random Wave Conjecture
Externí odkaz:
http://arxiv.org/abs/2408.14815
Autor:
Warner, Garth
The purpose of this book is two fold. (1) To give a systematic account of classical "zero theory" as developed by Jensen, P\'olya, Titchmarsh, Cartwright, Levinson and others. (2) To set forth developments of a more recent nature with a view toward t
Externí odkaz:
http://arxiv.org/abs/2408.00961
Autor:
Lodone, Giovanni
An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate
Comment: 15 pages, 10 figures
Comment: 15 pages, 10 figures
Externí odkaz:
http://arxiv.org/abs/2407.07910
Autor:
Gun, Sanoli, Lunia, Rashi
Publikováno v:
Bulletin of the London Mathematical Society, vol. 56, 2024, 1570-1586
In 2008, Soundararajan showed that there exists a normalized Hecke eigenform $f$ of weight $k$ and level one such that $$ L(1/2, f ) ~\geq~ \exp\Bigg( (1 + o(1)) \sqrt{\frac{2\log k}{\log\log k} }\Bigg) $$ for sufficiently large $k \equiv 0 \pmod{4}$
Externí odkaz:
http://arxiv.org/abs/2405.02428
Autor:
Kiuchi, Isao, Eddin, Sumaia Saad
Let $\gcd(m,n)$ denote the greatest common divisor of the positive integers $m$ and $n$, and let $\mu$ represent the M\" obius function. For any real number $x>5$, we define the summatory function of the M\" obius function involving the greatest comm
Externí odkaz:
http://arxiv.org/abs/2403.02792
Autor:
Kaneko, Masanobu, Tsumura, Hirofumi
We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double $T$-values, and some double $L$-values. Also presented is a connection-type for
Externí odkaz:
http://arxiv.org/abs/2401.03213
Autor:
Xu, Ce, Zhao, Jianqiang
In this paper we shall consider a few variants of the motivic multiple zeta values of level two by restricting the summation indices in the definition of multiple zeta values to some fixed parity patterns. These include Hoffman's multiple $t$-values,
Externí odkaz:
http://arxiv.org/abs/2310.16041