The mean square of the product of a Dirichlet $L$-function and a Dirichlet polynomial

Autor: Henryk Iwaniec, J. Brian Conrey, Kannan Soundararajan

Publikováno v: Funct. Approx. Comment. Math. 61, no. 2 (2019), 147-177

We establish an analogue of a conjecture of Balasubramanian, Conrey, and Heath-Brown for the family of all Dirichlet characters with conductor up to $Q$. This forms another application of our work in developing an asymptotic large sieve.
Comment

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e76a731ec9f2fd8cfc2c2a5ec3569df3
https://projecteuclid.org/euclid.facm/1572055494

The highest lowest zero of general L-functions

Autor: J. Brian Conrey, Stefan Lemurell, Sally Koutsoliotas, Hiroyuki Yoshida, Jonathan Bober, Michael O. Rubinstein, David W. Farmer, Akio Fujii

Publikováno v: Bober, J W, Conrey, J B, Farmer, D W, Fujii, A, Koutsoliotas, S, Lemurell, S, Rubinstein, M & Yoshida, H 2015, ' The highest lowest zero of general L-functions ', Journal of Number Theory, vol. 147, pp. 364-373 . https://doi.org/10.1016/j.jnt.2014.07.023

Stephen D. Miller showed that, assuming the generalized Riemann Hypothesis, every entire $L$-function of real archimedian type has a zero in the interval $\frac12+i t$ with $-t_0 < t < t_0$, where $t_0\approx 14.13$ corresponds to the first zero of t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc8b8a28a1e156a967490feaf806db40
https://doi.org/10.1016/j.jnt.2014.07.023

Autocorrelation of ratios of $L$-functions

Autor: David W. Farmer, Martin R. Zirnbauer, J. Brian Conrey

Publikováno v: Web of Science

We give a new heuristic for all of the main terms in the quotient of products of L-functions averaged over a family. These conjectures generalize the recent conjectures for mean values of L-functions. Comparison is made to the analogous quantities fo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b94de35a0f63e1145d9b6dc6946727f1
https://doi.org/10.4310/cntp.2008.v2.n3.a4

Real zeros of quadratic Dirichlet L-functions

Autor: Kannan Soundararajan, J. Brian Conrey

Publikováno v: Inventiones mathematicae. 150:1-44

We show that for a positive proportion of real primitive Dirichlet characters chi, the associated Dirichlet L-function L(s,chi) has no zeros on the positive real axis. Prior to this it was not known whether or not there were infinitely many L-functio

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::24c91d2f69671eacb2f92dfd2742cd8d
https://doi.org/10.1007/s00222-002-0227-x

Spectral line shapes in systems undergoing continuous frequency modulation

Autor: J. Brian Conrey, Lionel M. Raff, Ronald D. Kay, Donald L. Thompson, Dan C. Sorescu, A. Keith Jameson, Paras M. Agrawal

Publikováno v: The Journal of Chemical Physics. 105:2686-2700

The power spectrum line shapes for oscillators undergoing a continuous modulation of the vibrational frequency are investigated. It is shown that the single, sharp line normally characteristic of such systems broadens and exhibits a wealth of fine st

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::238bf28613eb533dac5664af3185cda9
https://doi.org/10.1063/1.472132