The Internet facilitates people’s lives. You can do almost anything online: manage your bank deposits, buy food, order air tickets, and so on. This means that the account is important to you. Set strong and different passwords for each service. If you have many accounts, then here is a suggestion: make use of a password manager.

**jstor**.org/stable/2004376

CALCULATION OF DIRICHLET L-FUNCTIONS 491 (4) x(B3) = exp (27ri3j/hi), O < ?1 < hi; j = 1, **, R. Clearly, the R-tuple of nonnegative integers ,Bj determines and is determined by the character x. Using this representation, it is now easy to see that the characters form a group isomorphic to M(k) under the mapping x B10 – e -BROR, (where

**jstor**.org/stable/2414163

Evaluation of Dirichlet L-functions 123 The L-functions, L(s, X), may be continued analytically over Ms < 1 and for primitive characters-they satisfy the functional equation L(8, X) = 2sk-sents-r(i -8) sin -1rsL(1 -s,-) (1.3) if 1) +1 and L(8, x) = 2sk-sers-lr(i -8 ) cos -7r8L(l -s, X) (1.4) if x(-1) =-1.

**jstor**.org/stable/2005484

On Small Zeros of Dirichiet **L**–**Functions** By Peter J. Weinberger To D. H. Lehmer for his 70th birthday Abstract. A method is given for calculating the value **of Dirichlet L**–**functions** near the real axis in the critical strip. As an application, some zeros for zeta **functions** …

**jstor**.org/stable/1989387

include as a special case (a = b = 1) the Riemann **function** c(s), characterized by Gram as "une des plus remarquables acquisitions de **l**‘analyse moderne"; while simple linear combinations of Z(a, b, s) for b = 1, 2, , a-1, when a is a fixed integer, give the **Dirichlet L**–**functions**. All of these special **functions**,

**jstor**.org/stable/2415308

Approximate functional equation for Dirichlet L-functions 225 whzere NX = [V(t/2irk) + 2], R < At, c = X(a) cos lba where ~~~ ~~~~~k-1i7T a I1 and SI? = n02i+ n ? Epi! (2k) VJP)(20k(), with _~Sk kC with b-1 in(phx(n)-Phe?7r(2- 2 An k ) with Vr(A) = sin 17T(2A +k) n=2 For X(-1) =-1, we have exp( Qi) for exp(7 ri) in the third term of (11),