# U

UEHARA T.,
[1] Vandiver's congruences for the relative class number of an imaginary abelian field, Mém. Fac. Sci. Kyushu Univ., Ser. A, 29 (1975), 249-254.
Z313.12006; M52#8087; R1976,3A140

[2] Bernoulli numbers in real quadratic fields (A remark on a work of H. Lang), Rep. Fac. Sci. Eng. Saga Univ., Math. 4 (1976), 1-5.
Z333.12006; M53#8017; R1976,11A195

[3] Fermat's conjecture and Bernoulli numbers, Rep. Fac. Sci. Eng. Saga Univ., Math., No. 6, (1978), 9-14.
Z379.10014; M80a:12008; R1978,12A179

[4] On p-adic continuous functions determined by the Euler numbers, Rep. Fac. Sci. Eng. Saga Univ., Math., No. 8, (1980), 1-8.
Z426.10015; M81e:12020; R1980,10A270; [5] On the Bernoulli numbers and the circular units of cyclotomic fields, Number Theory, Proc. Sympos., Koyoto, (1980), 47-60.

[6] On some congruences for generalized Bernoulli numbers, Rep. Fac. Sci. Eng. Saga Univ., Math., (1982), No. 10, 1-8.
Z493.12008; M83m:12014; R1982,10A306; [7] On cyclotomic units connected with p-adic characters, J. Math. Soc. Japan, 37 (1985), no. 1, 65-77.
Z547.12002; M87a:11110; R1985,8A399

[8] A certain congruence relation between Jacobi sums and cyclotomic units. Class numbers and fundamental units of algebraic number fields, Proc. Int. Conf. (Katata, 1986), pp. 33-52, Nagoya Univ., Nagoya, 1986.
Z615.12006; M88m:11088

[9] On a congruence relation between Jacobi sums and cyclotomic units, J. Reine Angew. Math., 382 (1987), 199-214.
Z646.12002; M89a:11113; R1988,6A304

[10] On the first generalized Bernoulli number, Rep. Fac. Sci. Engrg. Saga Univ. Math., 24 (1995), no. 1, 11-21.
Z838.11017; M96j:11021; R1996,4A271

UENO K., NISHIZAWA M.,
[1] Multiple gamma functions and multiple $q$-gamma functions, Publ. Res. Inst. Math. Sci., 33 (1997), no. 5, 813-838.
Z907.33001; M99b:33003; R1999,4B9

UGRIN-SPARAC D.,
[1] Some number theoretic applications of certain polynomials related to Bernoulli polynomials (Romanian summary), An. Sti. Univ. "Al. I. Cuza" Iasi Sec. I a Mat. (N.S.), 14 (1968), 259-276.
Z199.36402; M41#1664; R1970,2A86

[2] Lower bounds for sums of powers of different natural numbers expressed as functions of the sum of these numbers, J. Reine Angew. Math., 245 (1970), 74-80.
Z206.05503; M43#3228; R1971,5A105

[3] One particular class of Eulerian numbers of higher order and some allied sequences of numbers, Publ. Math. Debrecen, 18 (1971), 23-35.
Z267.10010; M54#10135; R1973,6V304

[4] Some properties of numbers M, N and L, Glasnik Mat., 14 (34) (1979), no. 2, 201-211.
Z429.10006; M83c:10019; R1980,8A85

UHLER H.S.,
[1] The coefficients of Stirling's series for $\log \Gamma(x)$. Proc. Nat. Acad. Sci., 28 (1942), 59-62.
M3-275g

ULLOM S.V.,
[1] Upper bounds for p-divisibility of sets of Bernoulli numbers, J. Number Theory, 12 (1980), 197-200.
Z449.10009; M81h:10019; R1981,2A127

UNDERWOOD R.S.,
[1] An expression for the summation $\sum_{m=1}^n m^p$, Amer. Math. Monthly, 35 (1928), 424-428.
J54.0104.01

URBANOWICZ J.,
[1] On the divisibility of generalized Bernoulli numbers. Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), pp. 711-728, Contemp. Math., 55, Amer. Math. Soc., Providence, R.I., 1986.
Z596.12002; M88b:11012; R1987,3A136

[2] On the divisibility of $w_{m+1}(F^+){\zeta}_{F^+}(-m)$ for cyclotomic fields F, Comm. Algebra, 16 (1988), no.7, 1315-1323.
Z661.12001; M89k:11100; R1988,11A366

[3] On the equation $f(1)1^k+f(2)2^k+ \cdots +f(x)x^k+R(x)=By^2$, Acta Arith., 51 (1988), no. 4, 349-368.
Z661.10026; M90b:11025; R1989,8A106

[4] Remarks on the equation $1^k+2^k+ \cdots +(x-1)^k=x^k$, Nederl. Akad. Wetensch. Indag. Math., 50 (1988), no. 3, 343-348.
Z661.10025; M90b:11026; R1989,2A89

[5] Connections between $B_{2,\chi}$ for even quadratic Dirichlet characters $\chi$ and class numbers of appropriate imaginary quadratic fields. I, II. Compositio Math., 75 (1990), no.3, 247-270, 271-285. Corrig.: Compositio Math., 77 (1991), no. 1, 119-125.
Z706.11058; M92a:11134a; R1991,3A215

Z706.11059; M92a:11134b; R1991,8A433

[6] On the $2$-primary part of a conjecture of Birch-Tate. Acta Arith., 43 (1983),no. 1, 69-81.
Z529.12008; M85f:11080; R1984,8A297

[7] A generalization of the Lerch-Mordell formulas for positive discriminants. Colloq. Math., 59 (1990), no. 2, 197-202.
Z729.11050; M91m:11103

[8] On some new congruences between generalized Bernoulli numbers, I. Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, Années 1989/90-1990/91, No.4, 23pp., (1991).
Z748.11017; M93m:11111

[9] On some new congruences between generalized Bernoulli numbers, II. Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, 1989/90-1990/91, No.5, 24pp., (1991). Corrigendum ibid., 1992/93-1993/94, 3 pp.
Z748.11018; M93m:11111

[10] Remarks on the Stickelberger ideals of order 2. Algebraic $K$-theory, commutative algebra, and algebraic geometry. Proc. Joint US-Italy Seminar, Santa Margherita Ligure/Italy 1989, Contemp. Math., 126 (1992), 179-192.
Z756.11040; M93e:11139; R1993,7A290

[11] On Diophantine equations involving sums of powers with quadratic characters as coefficients, I. Compositio Math. 92 (1994), no. 3, 249-271.
Z810.11017; M96f:11054

[12] On Diophantine equations involving sums of powers with quadratic characters as coefficients. II. Compositio Math. 102 (1996), no. 2, 125-140.
Z960.35749; M97m:11047; R1997,10A186

URBANOWICZ J., WILLIAMS K.S.,
[1] Congruences for $L$-functions. Mathematics and its Applications, 511. Kluwer Academic Publishers, Dordrecht, 2000. xii+256 pp. ISBN: 0-7923-6379-5
Z0972.11001; M2001k:11209