On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L-functions

Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions

et E be an elliptic curve defined over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we describe a reinterpretation of the Equivariant Tamagawa Number Conjecture (‘ETNC’) for E, F/k and p as an explicit family of p-adic congruences involving values of derivatives of the Hasse-Weil L-functions of twists of E, norma...

Congruences between Selmer groups ∗

The study of congruences between arithmetically interesting numbers has a long history and plays important roles in several areas of number theory. Examples of such congruences include the Kummer congruences between Bernoulli numbers and congruences between coefficients of modular forms. Many of these congruences could be interpreted as congruences between special values of L-functions of arith...

Twisted L-Functions and Monodromy

Computing Annihilators of Class Groups from Derivatives of L-functions

We computationally verify that certain group ring elements obtained from the first derivatives of abelian L-functions at the origin annihilate ideal class groups. In our test cases, these ideal class groups are connected with cyclic extensions of degree 6 over real quadratic fields.

on translation of phatic communion and socio-cultural relationships between the characters of the novels

phatic communion is a cultural concept which differs across cultures. according to hofstede (2001), the u.s. tends to have individualistic culture; however, asian countries tend to have collectivistic cultures. these cultures view phatic communion differently. in individualistic cultures like u.s., phatic communion reflects speakers’ socio-cultural relationships in conversations. to see whether...