when was jesus born?

jesus was born when "herod the king" gospel matthew 2.1 that is 37 bc, after herod the governor. this is after julius ceasar died in 44 bc [senators killed him but died] so anything before herod is tooo far to bother with outside of college history degree.
ROMAN senate appointed herod king of judea and he conquered it in 37 bc. he died in 4 bc and jesus was born before his death if gospel is true.
if number count is true year 2018, then gospel lied because herod died 4 bc so after herod and say in days of herod would be a lie or gospel true and more than 2018 years ago at latest 4 bc but maybe earlier in past before 4 bc when we know herod died.  then his son ar. took over=archelaus mat. 2.22, reigned in judea between 4 BC and 6= (-4)-(6). but not galilee in 4 bc
philip ruled... "Herod Phillip Antipas Tetrarch of Galilee" from 4 bc, brother of archeluas both sons of herod and in this detail he gospel of luke is inaccurate because herod was the title for many and philip in galilee but luke wrote inaccurately cut herod philip into 2 oops.
not "brother philip" but philip brother of archelaus the name in matthew 2.22 later see
https://www.geni.com/people/Herod-Tetrarch-of-Galilee-and-Perea/6000000002187718440
at least the emperor is good luke 2.1 "augustus ceasar" perhaps month august named for him?  from year -27 named augustus. ruled 31 bc until 14 around 45 years=44 cuz january 1 bc until january 2 ad  is only 24 months.
+luke 3.1 "tiberius ceasar" ruled years 14-37. so 15 of t. means year 29 when jesus was at least 33 when jesus "around 30 in that chapter 3.23"
another emperor mentioned is claudius 41-54 in acts 18.2
from the end of book chronicles until first ceasar mentioned in gospel luke 2, were empires
first babylonian empire nebuchadnezer ruled from city babylon  ruling jerusalem occupation, empire was strong from "The Babylonian Empire was the most powerful state in the ancient world after the fall of the Assyrian empire (612 BCE). Its capital Babylon was beautifully adorned by king Nebuchadnezzar, who erected several famous buildings. Even after the Babylonian Empire had been overthrown by the Persian king Cyrus the Great (539)" so 612 bc until -539 sometime in between captured jerusalem and year numbers in bible certainly false we know about mesa and neb. so false numbers.
source
http://www.livius.org/articles/place/babylonian-empire
persian empire from 539 v as above ruling until macedonia greek empire 332 bc
persian strong -539 until -330
greek strong -332 until -164 hasmonean dynasty self-rule of jews until -63 roman. as above too far to elaborate and roman ruled until emperor augustus as above.
which books tell the story of that era?
josephus and the ancient jews had books called "macabees" included in septuagint and hence in catholic bible later jews and protestants removed the books which the jews once included as preserved in josephus.
ferguson wrote about jewish culture
under rome pages 527-582.backgrounds of early christianity  1993 and 2003
also pfeiffer  between the testaments 1959 and bickerman  from ezra to last macabee 1962
the dead sea scrolls were translated to english vermes 1987.
other books describing this era but too early for christians unless they want to fill the gap from nebucadnezer, jagersma from alexander to bar kokba 1985
tcherikover hellinistic 1959 or hebrew title jews under greek and rome 1961 old same author 1982
later regarding herod perowne  herod 1956 or stern  hebrew title herod kingdom 1992, and before herod if you want h=juda hasmonean 1995