Greenberg's conjecture for Dirichlet characters of order divisible by $p$

Newton Polygons and P-divisible Groups: a Conjecture by Grothendieck

Bloch-kato Conjecture and Main Conjecture of Iwasawa Theory for Dirichlet Characters

The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values” of L-functions in terms of cohomological data. The main conjecture of Iwasawa theory describes a p-adic L-function in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for L-functions attached to Dirichlet characters. We use the...

Density Functions for Families of Dirichlet Characters

As M. Rubinstein [Ru] has already considered all primitive quadratic characters with prime conductor q ∈ [N, 2N ], we do not include our notes of this case. For these families we show the 1-Level Densities agree with the Unitary Group for even Schwartz functions φ̂ with supp(φ̂) ⊂ (−2, 2). We conclude with an appendix on “reasonable” assumptions which would allow us to extend the support of the t...

study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour

this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...

A Note on Dirichlet Characters

Denoting by r(k, m, p) the first occurrence of m consecutive fcth power residues of a prime p = 1 (mod k), we show that r(k, m, p) > c log p for infinitely many p (c is an absolute constant) provided that k is even and m ä 3.