# X-Y-Z

XIN XIAO LONG, ZHANG JIAN KANG,
[1] Some identities connecting Euler numbers and Bernoulli numbers (Chinese), Pure Appl. Math., 9 (1993), no. 1, 23-28.
Z849.11022; M94j:11024

YAGER R.I.,
[1] A Kummer criterion for imaginary quadratic fields, Compos. Math., 47 (1982), no. 1, 31-42.
Z506.12008; M83k:12008; R1983,2A276

YAGISHITA K.,
[1] On the Diophantine equation $\alpha^l + \beta^l = c \gamma^l$, TRU Math., 7 (1971), 5-10.
Z256.10014; M46#7161; R1973,5A149

YALAVIGI C.C.,
[1] Bernoulli and Lucas numbers, Math. Education, 5 (1971), A99-A102.
M46#131

[1] An experimental theory of numbers (The prime factors of the numerators of Bernoulli numbers), J. Fac. Eng. Ibaraki Univ., 35 (1987), 159-170.
R1988.10A111

[2] An approach to Wieferich's condition, C. R. Math. Rep. Acad. Sci. Canada, 13 (1991), no. 2-3, 87-92.
Z731.11019; M92f:11052

YAMAGUCHI I.,
[1] On Fermat's last theorem, TRU Math., 3 (1967), 13-18.
Z167.31603; M36#6350; R1968,10A91

[2] On generalized Fermat's last theorem, TRU Math., 6 (1970), 29-32.
Z242.10009; M46#8974; R1973,11A168

[3] On a property of the irregular class group in a properly $l$-th cyclotomic field, TRU Math., 7 (1971), 21-24.
Z252.12004; M47#3352; R1973,5A357

[4] On a Bernoulli numbers conjecture, J. Reine Angew. Math., 288 (1976), 168-175.
Z333.10005; M54#12628; R1977,6A100

[5] On the units in a $l^\nu$-th cyclotomic field, TRU Math., 13 (1977), no. 2, 1-12.
Z379.12003; M58#584; R1978,10A250

[6] Sympathetic Number Theory - The beautiful cyclotomic fields theory and Bernoulli numbers (Japanese), Sangyotosho Co. Ltd., 1994.

YAMAMOTO S.: see SHIRATANI K., YAMAMOTO S.

YANG BI CHENG,
[1] Formulas for sums of homogeneous powers of natural numbers related to the Bernoulli numbers (Chinese). Math. Practice Theory, 1994, no. 4, 52-56, 74.
M96c:11026

YANG BI CHENG, ZHU YUN HUA,
[1] Inequalities for the Hurwitz zeta-function on the real axis (Chinese), Acta Sci. Natur. Univ. Sunyatseni 36 (1997), no. 3, 30-35.
M99h:11101

YANG BI CHENG: see also ZHU YUN HUA, YANG BI CHENG,

YANG HUI,
[1] The operator l and its applications. I. A generalization of the Bernoulli polynomials, J. Math. (Wuhan), 1 (1981), no. 2, 195-206. (Chinese. English summary.)
Z519.33010; M83k:39004

Yang, Qian Li,
[1] On a congruence of the Euler numbers. (Chinese) J. Northwest Univ. 36 (2006), no. 3, 351-352.

Yang, Sheng Liang; Qiao, Zhan Ke; Ma, Cheng Ye,
[1] Relationship between Bernoulli polynomials and power sum polynomials. (Chinese) J. Lanzhou Univ. Technol. 32 (2006), no. 4, 130--132.

YAU STEPHEN S.-T.: see LIN KE-PAO, YAU STEPHEN S.-T.

Yi, Yuan,
[1] Some identities involving Bernoulli numbers and Euler numbers. Sci. Magna 2 (2006), no. 1, 102--107.
M2007c:11023

YOKOI H.,
[1] On the distribution of irregular primes, J. Number Theory, 7 (1975), 71-76.
Z297.10034; M51#385; R1976,7A180

YOKOYAMA S.: see SHIRATANI K., YOKOYAMA S.

YOR M.: see PITMAN J., YOR M.

YOSHIDA H.,
[1] On absolute CM-periods. II, Amer. J. Math. 120 (1998), no. 6, 1199-1236.
Z0919.11077; M2000a:11093

[2] Absolute CM-periods. Mathematical Surveys and Monographs, 106. American Mathematical Society, Providence, RI, 2003. x+282 pp. ISBN 0-8218-3453-3.
M2004j:11057

YOSHIDA M.,
[1] A representation of the Bernoulli numbers $B_n$ and the tangent numbers $T_n$. SUT J. Math., 26 (1990), no. 2, 207-219.
Z746.11013; M92k:11021; R1991,11V421

YOUNG N.E.: see MILLAR J., SLOANE N.J.A., YOUNG N.E.

YOUNG P.T.,
[1] Congruences for Bernoulli, Euler, and Stirling numbers. J. Number Theory, 78 (1999), no. 2, 204-227.
Z939.11014; M2000i:11038

[2] Kummer congruences for values of Bernoulli and Euler polynomials. Acta Arith. 99 (2001), no. 3, 277-288.
Z0982.11008; M2002g:11021; R02.04-13A.117

[3] On the behavior of some two-variable $p$-adic $L$-functions. J. Number Theory 98 (2003), no. 1, 67-88.

[4] Degenerate and $n$-adic versions of Kummer's congruences for values of Bernoulli polynomials. Discrete Math. 285 (2004), no. 1-3, 289-296.

YOUNG R.M.: see NUNEMACHER J., YOUNG R.M.

YU JING,
[1] A cuspidal class number formula for the modular curves $X_1(N)$, Math. Ann., 252 (1980), no. 3, 197-216.
Z426.12003; Z426.12003;436.12002; M82b:10030; R1981,6A377

[2] Transcendence and special zeta values in characteristic $p$. Ann. Math. (2), 134 (1991), no. 1, 1-23.
Z734.11040; M92g:11075

YU JING, YU JIU-KANG,
[1] A note on a geometric analogue of Ankeny-Artin-Chowla's conjecture, Number theory (Tiruchirapalli, 1996), 101-105, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998.
Z896.11047; M98g:11131

YÜ WÊN CH'ING: see EIE MINKING

Yuan, Pingzhi,
[1] A conjecture on Euler numbers. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 9, 180-181.
M2005f:11030

ZAGIER D.B.,
[1] Valeurs des fonctions zêta des corps quadratiques réels aux entiers négatifs. Journées Arithmétiques de Caen (Univ. Caen, 1976), pp. 135-151. Astérisque No. 41-42, Soc. Math. France, Paris, 1977.
Z359.12012; M56#316; R1977,12A140

[2] Zetafunktionen und quadratische Körper. Eine Einführung in die höhere Zahlentheorie. Springer-Verlag, Berlin, 1981. viii + 144 pp.
Z459.10001; M82m:10002; R1982,3A107

[3] Hyperbolic manifolds and special values of Dedekind zeta-functions, Sonderforschungsbereich 40 Theor. Math., Univ. Bonn, 1984.

[4] Hyperbolic manifolds and special values of Dedekind zeta-functions, Invent. Math., 83 (1986), no. 2, 285-301.
Z591.12014; M87e:11069; R1986,6A500

[5] Periods of modular forms and Jacobi theta functions. Max-Planck-Institut für Math. Bonn, MPI/89-56, 15 pp.

[6] Periods of modular forms and Jacobi theta functions, Invent. Math., 104 (1991), no. 3, 449-465.
Z742.11029; M92e:11052

[7] On the values at negative integers of the zeta-function of a real quadratic field. Enseignement Math. (2), 22 (1976), 55-95.
Z334.12021; M53#10742; R1976/77,12A163

[8] Polylogarithms, Dedekind zeta functions, and the algebraic $K$-theory of fields. Arithmetic algebraic geometry, Proc. Conf., Texel/Neth. 1989, Prog. Math., 89 (1991), 391-430.
Z728.11062; M92f:11161

[9] Elementary aspects of the Verlinde formula and of the Harder- Narasimhan-Atiyah-Bott formula. Max-Planck-Institut für Math., Bonn, 1994, no.5, 16 pp.

[10] A modified Bernoulli number, Nieuw Arch. Wisk. (4), 16 (1998), no. 1-2, 63-72.
Z0964.11015; M99i:11013; R1999,2V229

ZAGIER D.: see also KANEKO M., ZAGIER D.

ZAGIER D.: see also KOHNEN W., ZAGIER D.

ZARNKE C.: see BEACH B., WILLIAMS H., ZARNKE C.

ZECH TH.,
[1] Potenzsummen und Bernoullische Zahlen, Z. Angew. Math. Mech., 34 (1954), 119-120.
Z56.01307; M15-855e; R1955,838

ZEITLIN D.,
[1] Remarks on a formula for preferential arrangements, Amer. Math. Monthly, 70 (1963), 183-187.
Z116.01102; M26#4928; R1964,12A143

[2] On the sums $\sum_{k=0}^nk^p$ and $\sum_{k=0}^n(-1)^kk^p$, Proc. Amer. Math. Soc., 15 (1964), 642-647.
Z123.00102; M29#5010; R1967,1V164

ZELENOV E.I.: see VLADIMIROV V.S. et al.

ZELLER CHR.,
[1] De numeris Bernoulli eorumque compositione ex numeris integritis et reciprocis primis, Bull. sci. math. et astr., 5 (1881), 195-215.
J13.0190.02

ZENG JIANG,
[1] Sur quelques propriétés de symétrie des nombres de Genocchi. (French) [On some symmetry properties of Genocchi numbers] Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993). Discrete Math. 153 (1996), no. 1-3, 319-333.
Z870.05002; M97k:05015

[2] The Akiyama-Tanigawa algorithm for Carlitz's $q$-Bernoulli numbers. Integers 6 (2006), A5, 10 pp. (electronic).
M2007a:11026

^M Zeng, Jiang; Zhou, Jin,
[1] A $q$-analog of the Seidel generation of Genocchi numbers. European J. Combin. 27 (2006), no. 3, 364-381.
M2006k:05023

^M ZENG J.: see also DUMONT D., ZENG J.

ZENG J.: see also HAN GUO-NIU, ZENG JIANG

ZHANG JIAN KANG: see XIN XIAO LONG, ZHANG JIAN KANG

ZHANG J.-M.: see WONG R., ZHANG J.-M.

ZHANG JING, FANG JIAN PING,
[1] A generalization of Wolstenholme's theorem. (Chinese. English, Chinese summary) J. Nanjing Norm. Univ. Nat. Sci. Ed. 23 (2000), no. 1, 19-20.
Z1020.11004; M2001m:11012

ZHANG N.Y.,
[1] A representation of Riemann's zeta-function (Chinese), J. Math. Res. Exposition (1982), no. 4, 119-120.
Z506.10033; M84c:10037

[2] The Euler constant and some sums associated with the zeta function. (Chinese). Math. Practice Theory, (1990), no. 4, 62-70.
M92a:11098

ZHANG N.Y.: see also WILLIAMS K.S., ZHANG N.Y.

ZHANG PING: see SAGAN B.E., ZHANG PING

ZHANG SHANJIE, JIN JIANMING,
[1] Computation of special functions. John Wiley & Sons, Inc., New York, 1996. xxvi+717 pp. ISBN 0-471-11963-6
Z0865.33001; M97m:65001

Zhang, Tianping; Ma, Yuankui,
[1] On generalized Fibonacci polynomials and Bernoulli numbers. J. Integer Seq. 8 (2005), no. 5, Article 05.5.3, 6 pp. (electronic).
M2006h:11015

ZHANG WEI RONG,
[1] Using a Newtonian formula to prove a theorem of Euler. (Chinese.) J. Nanjing Norm. Univ. Nat. Sci. Ed. 22 (1999), no. 1, 16-17.
M2000h:11021

ZHANG WENPENG,
[1] On the several identities of Riemann zeta-function, Chinese Sci. Bull., 36 (1991), no. 22, 1852-1856.
Z755.11026; M92m:11086

[2] Some identities for Euler numbers (Chinese), J. Northwest Univ., 22 (1992), no. 1, 17-20.
Z886.11011; M93h:11024

[3] Some identities involving the Euler and the central factorial numbers, Fibonacci Quart. 36 (1998), no. 2, 154-157.

[4] On the general Dedekind sums and one kind identities of Dirichlet $L$-functions. (Chinese. English, Chinese summary) Acta Math. Sinica 44 (2001), no. 2, 269-272.
M2002c:11106

ZHANG WENPENG: see also LIU HUANING, ZHANG WENPENG.

ZHANG XIANG DE: see WANG TIAN MING, ZHANG XIANG DE

ZHANG XIAN KE,
[1] A congruence formula for the class number of a general fourth degree cyclic field, Kexue Tongbao (Chinese), 32 (1987), no. 23, 1761-1763.
M89g:11101

[2] Congruences of class numbers of general cubic cyclic number fields (Chinese. English summary). J. China Univ. Sci. Tech., 17 (1987), no. 2, 141-145.
Z631.12003; M88i:11076; R1987,12A291

[3] Congruences for class numbers of general cyclic quartic fields, Kexue Tongbao (Science Bulletin), 33 (1988), no. 22, 1845-1848.

[4] Congruences modulo 8 for class numbers of general quadratic fields $Q(\sqrt{m})$ and $Q(\sqrt{-m})$, J. Number Theory, 32 (1989), no. 3, 332-338.
Z693.12005; M90k:11137

[5] Ten formulae of type Ankeny-Artin-Chowla for class numbers of general cyclic quartic fields, Sci. China Ser. A, 32 (1989), no. 4, 417-428.
Z669.12005; M91b:11112

ZHANG ZHIZHENG,
[1] Relation between two kinds of numbers and its applications, Gongcheng Shuxue Xuebao 13 (1996), no. 1, 114-116.
M97g:11017; R1997,3V221

ZHANG ZHIZHENG, GUO LIZHOU,
[1] Recurrence sequences and Bernoulli polynomials of higher order, Fibonacci Quart., 33 (1995), no. 4, 359-362.
Z831.11023; M96c:11027; R1996,5A119

ZHANG ZHIZHENG, JIN JINGYU,
[1] Some identities involving generalized Genocchi polynomials and generalized Fibonacci-Lucas sequences, Fibonacci Quart., 36 (1998), no. 4, 329-334.
Z0973.11018; R1999,4V225

Zhang, Zhizheng; Wang, Jun,
[1] Bernoulli matrix and its algebraic properties. Discrete Appl. Math. 154 (2006), no. 11, 1622--1632.

ZHANG ZHIZHENG: see also WANG TIANMING, ZHANG ZHIZHENG

ZHANG ZHIZHENG: see also LIU MAI XUE, ZHANG ZHI ZHENG

ZHENG YU MIN, LUO QIU MING,
[1] The recursion formulas of higher-order Bernoulli numbers. (Chinese) Math. Practice Theory 33 (2003), no. 8, 116-119.

Zhao, Feng-Zhen; Wang, Tianming,
[1] Values of Nörlund Euler polynomials and Nörlund Bernoulli polynomials. C. R. Math. Acad. Sci. Soc. R. Can. 26 (2004), no. 4, 97-101.
M2005h:11041

ZHENG ZHIYONG,
[1] The Petersson-Knopp identity fo the homogeneous Dedekind sums, J. Number Theory, 57 (1996), no. 2, 223-230.
Z847.11021; M97c:11050

ZHBIKOVSKII A.K.,
[1] Teorema Silvestra otnositel'no bernullievykh chisel [Sylvester's theorem concerning Bernoulli numbers]. Vestnik matem. nauk, 1 (1862), no. 13, 109-110.

[2] K teorii chisel Bernulli [On the theory of Bernoulli numbers]. Mat. Sbornik, 10 (1882), no. 2, 127-166.

ZHU WEI YI,
[1] An identical relation between the Bernoulli numbers and the Euler numbers. (Chinese) J. Ningxia Univ. Nat. Sci. Ed. 22 (2001), no. 4, 370-371.
Z1021.11004

ZHU YUN HUA, YANG BI CHENG,
[1] An improvement of Euler's summation formula and some inequalities for sums of powers (Chinese), Acta Sci. Natur. Univ. Sunyatseni 36 (1997), no. 4, 21-26.
Z902.40002; M99i:40003

ZHU YUN HUA: see also YANG BI CHENG, ZHU YUN HUA

ZIA-UD-DIN M.,
[1] Recurrence formulae for Bernoulli's numbers, Math. Student, 3 (1935), 141-151.
J61.0985.02; Z14.10202

[2] Some more formulae for the Bernoullian mumbers. Math. Student 15 (1938), 81-157.
Z019.10402

ZIMMER H.G.,
[1] Computational problems, methods and results in algebraic number theory, New York, Lecture Notes in Math., No. 262, 1972.
Z231.12001; M48#2107; R1972,10A225

ZUBER M.,
[1] Propriétés de congruence de certaines familles classiques de polynômes, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 8, 869-872.
Z762.11005; M94b:11025

[2] Propriétés $p$-adiques de polynômes classiques, Thèse, Université de Neuchatel, 1992.

[3] Suites de Honda, Ann. Math. Blaise Pascal 2 (1995), no. 1, 307-314.
Z833.46062; M96k:11143

ZUDILIN W.,
[1] Algebraic relations for multiple zeta values. Russian Math. Surveys 58 (2003), no. 1, 1-20