Temperature inversion symmetry in gauge-Higgs unification models

We study the temperature inversion symmetry R → 1/T for the finite-temperature effective potential of the N=1, d=5 supersymmetric SU(3) _c ×SU(3) _w model on the orbifold S ¹ /Z ₂ . For the value of the Wilson line parameter α = 1 (SU(2) _L breaks to U′(1)), we show that the effective potential contains a symmetric part and an antisymmetric part under ξ → 1/ξ, ξ = RT. For α = 0 (SU(2) _L is preserved in this case), we find that the only contribution to the effective potential that breaks the temperature inversion symmetry comes from the fermions in the fundamental representation of the gauge group with the Z ₂ parities (+, +) or (−,−). This is interesting because it implies that the bulk effective potential corresponding to models with fundamental fermions localized at a fixed point in the orbifold (and models with no bulk fundamental fermions) has the temperature inversion symmetry. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 109–130, April, 2009.     

A Joint Limit Theorem for the Riemann Zeta-Function in the Space of Analytic Functions

In this paper, we prove a joint limit theorem for the Riemann zeta-function in the space of analytic functions in the sense of weak convergence of probability measures.     

Partial resolutions and the zeta-function of a singularity

We give a generalization of N. A'Campo's formula for the zeta-function of the monodromy of a singularity and show some examples of its applications. Received: March 25, 1966     

Growth of the Lerch zeta-function

It is believed that the Lindelöf hypothesis is also true for the Lerch zeta-function. Here we present results supporting this conjecture. We first consider the growth of the Lerch zeta-function assuming the generalized Lindelöf hypothesis for Dirichlet L-functions. We next prove that Huxleys exponent 32/205 in the Lindelöf hypothesis for the Riemann zeta-function holds also for the Lerch zeta-function.__________Partially supported by a grant from the Lithuanian State Science and Studies Foundation.Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 45–56, January–March, 2005.     

On alternating analogues of Tornheim’s double series II

In this paper, we evaluate the alternating analogues of Tornheim’s double series. This is an answer to the problem posed by Subbarao-Sitaramachandrarao, and can be regarded as an alternating analogue of the evaluation formula for Tornheim’s double series, given by Huard, Williams and Z. Nan-Yue. We also evaluate partial Tornheim’s double series.      

关于Hurwitz zeta—函数的四次均值

对ｓ＝σ＋ｉｔ，ζ（ｓ，ａ）是Ｈｕｒｗｉｔｚｚｅｔａ－函数，ζ１（ｓ，ａ）＝ζ（ｓａ）－ａ＾－ｓ，。本文的主要目的是用解析的方法给出了Ｈｕｒｗｉｔｚｚｅｔａ－函数四次均值较强的渐近公式。     

An explicit formula for the square of the Riemann zeta-function in the critical strip

In this article, we prove an explicit formula for |ζ(σ + iT)|², where ζ(s) is the Riemann zeta-function and 1/2 < σ < 1, which is an analogue of Jutila’s formula. Our proof differs from that of Jutila. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 381–398, July–September, 2007.     

Value distribution of the Lerch zeta-function with algebraic irrational parameter. II

In this paper, we obtain a joint limit theorem in the sense of weak convergence of probability measures on the complex plane for Lerch zeta-functions with algebraic irrational parameters and give an explicit form of the limit measure. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 482–496, October–December, 2007.     

On the Distribution of Integral Ideals and Hecke Gr¨ossencharacters

The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and Good＇s results on the distribution of Hecke GrSssencharacters are improved.