2 research outputs found
The distribution of prime ideals of imaginary quadratic fields
No full textAbstract. Let Q(x; y) be a primitive positive definite quadratic form with
integer coecients. Then, for all (s; t) 2 R2 there exist (m; n) 2 Z2 such that
Q(m; n) is prime and
Q(m- s; n - t) Q(s; t)0:53 + 1:
This is deduced from another result giving an estimate for the number of prime
ideals in an ideal class of an imaginary quadratic number eld that fall in a
given sector and whose norm lies in a short interval
The diocese of Coventry and Lichfield, 1603-1642
No full textThis thesis investigates religious life among the clergy and laity in the diocese of
Lichfield, 1603-1642, including the role of Puritans, Catholics and Church
Papists. Nicholas Tyacke has maintained that the implementation of Laudianism
in Charles I's reign proved contentious, an interpretation criticised by some
historians who aver that the Church continued to maintain a 'middle way'. This
study finds that the evidence from the diocese largely supports Tyacke's
interpretation.
Proto-Laudian reforms were implemented in the see some years before the
Laudian ascendancy through the episcopates of Neile and Overall. Every bishop
in the period who undertook a programme of reform met local hostility and
indifference, and sometimes the opposition of his ecclesiastical and lay superiors.
Every religious group underwent change and development. Puritans and
Catholics pursued strategies for survival, supported by their respective religious
networks. Official opposition often had the effect of strengthening their resolve
and confirming them in their beliefs. Local conformists' commitment to the
established Church deepened during this period. They respected the Church's role
as the official purveyor of religion, morality and the ecclesiastical rites of passage,
without evidencing much theological understanding.
In the 1630s Bishop Wright oversaw the Laudian programme of
sacramental, sacerdotal and liturgical reform, but his lack of organisation, zeal and
commitment frustrated Charles, Laud and some local diocesan officials. The
changes met resistance, which gathered strength with the collapse of the Personal
Rule and manifested itself either in a desire to return to the pre-Laudian Church,
or in its root and branch reform. The strength of an individual's anti-Catholicism
indicated which religious solution s/he supported. When war came, for the most
part Puritans predictably supported Parliament, but a number of moderate Puritans
supported the King. Even among the 'godly' fraternity allegiance could
sometimes be determined by a variety of considerations
