Scalar product of L-functions with Grössencharacters: its meromorphic continuation and natural boundary.
Séries de Dirichlet et fonctions automorphes
Séries d'Eisenstein et fonctions L de courbes elliptiques à multiplication complexe.
Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems
We give a simple proof of the Siegel-Tatuzawa theorem according to which the residues at s = 1 of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer-Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.
Simple zeros of the zeta function of a quadratic number field. I.
Small values of zeta-functions of quadratic fields.
Sobre el índice de irregularidad de los números primos.
Solution of the Classs Number Two Problem for Cyclotomic Fields.
Some Analytic Bounds for Zeta Functions and Class Numbers.
Some Analytic Estimates of Class Numbers and Discriminants.
Some Effective Cases of the Brauer-Siegel Theorem.
Some estimates in the theory of Dedekind Zeta-functions
Some functions related to the derivatives of the L-series of an elliptic curve at s=1
Some meromorphic functions associated to the S-unit equation
Some new maps and ideals in classical Iwasawa theory with applications
We introduce a new ideal of the p-adic Galois group-ring associated to a real abelian field and a related ideal for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a -tower of abelian fields, and is linked by explicit reciprocity to a third ideal studied more generally in [D. Solomon, Acta Arith. 143 (2010)]. This leads to a new and unifying framework for the Iwasawa theory of such fields including a real analogue of Stickelberger’s Theorem,...
Some problems in multidimensional analytic number theory
Some remarks on L-functions and class numbers
Spacing of zeros of Hecke L-functions and the class number problem
Special Values of Artin L-Series.
Standard relations of multiple polylogarithm values at roots of unity.