Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2018, Volume 98, Issue 1, pp. 27 - 37

...$ -adic gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated $_{3}F_{2...

supercongruences | truncated hypergeometric series | p-adic gamma functions | LEGENDRE POLYNOMIALS | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | HYPERGEOMETRIC-SERIES

supercongruences | truncated hypergeometric series | p-adic gamma functions | LEGENDRE POLYNOMIALS | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | HYPERGEOMETRIC-SERIES

Journal Article

Journal of Number Theory, ISSN 0022-314X, 05/2016, Volume 162, pp. 463 - 482

We study a special case of Kashio's p-adic logΓ-function, that we call LogΓp, which combines these of Morita and Diamond...

Volkenborn integral | p-adic [formula omitted]-function | P-adic log Γ-function | MATHEMATICS | p-adic log Gamma-function | Mathematics - Number Theory

Volkenborn integral | p-adic [formula omitted]-function | P-adic log Γ-function | MATHEMATICS | p-adic log Gamma-function | Mathematics - Number Theory

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 06/2019, Volume 15, Issue 5, pp. 991 - 1007

... ( τ ) by using p -adic log multiple gamma functions, and conjectured that the log p of a Gross...

The Gross-Stark conjecture | p -adic measures | multiple gamma functions

The Gross-Stark conjecture | p -adic measures | multiple gamma functions

Journal Article

Pacific journal of mathematics, ISSN 0030-8730, 2013, Volume 261, Issue 1, pp. 219 - 236

We define a function in terms of quotients of the p-adic gamma function which generalizes earlier work of the author on extending hypergeometric functions over finite fields to the p-adic setting...

Hypergeometric functions | Elliptic curves | Modular forms | P-adic gamma function | Trace of Frobenius | trace of Frobenius | MATHEMATICS | hypergeometric functions | GAUSSIAN HYPERGEOMETRIC-SERIES | modular forms | FINITE-FIELDS | p-adic gamma function | elliptic curves

Hypergeometric functions | Elliptic curves | Modular forms | P-adic gamma function | Trace of Frobenius | trace of Frobenius | MATHEMATICS | hypergeometric functions | GAUSSIAN HYPERGEOMETRIC-SERIES | modular forms | FINITE-FIELDS | p-adic gamma function | elliptic curves

Journal Article

Journal of Number Theory, ISSN 0022-314X, 08/2012, Volume 132, Issue 8, pp. 1770 - 1779

In this note we study the relationship between the power series expansion of the Dwork exponential and the Mahler expansion of the p-adic Gamma function...

Dwork exponential | p-Adic Gamma function | p-Adic L-functions | Mahler series | P-Adic l-functions | P-Adic gamma function | MATHEMATICS | Universities and colleges

Dwork exponential | p-Adic Gamma function | p-Adic L-functions | Mahler series | P-Adic l-functions | P-Adic gamma function | MATHEMATICS | Universities and colleges

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2014, Volume 140, pp. 181 - 195

In [12], McCarthy defined a function Gnn[⋯] using the Teichmüller character of finite fields and quotients of the p-adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special values of G22...

Characters of finite fields | Teichmüller character | p-Adic gamma function | Elliptic curves | Trace of Frobenius | Gauss sums | P-Adic gamma function | Teichmuller character | MATHEMATICS | GAUSSIAN HYPERGEOMETRIC-SERIES

Characters of finite fields | Teichmüller character | p-Adic gamma function | Elliptic curves | Trace of Frobenius | Gauss sums | P-Adic gamma function | Teichmuller character | MATHEMATICS | GAUSSIAN HYPERGEOMETRIC-SERIES

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2013, Volume 50, Issue 2, pp. 583 - 588

In this paper, we introduce the q-analogue of p-adic log gamma functions with weight alpha...

Modified q-Genocchi numbers with weight alpha and beta | Modified q-Euler numbers with weight alpha and beta | p-adic log gamma functions | POLYNOMIALS | INTEGRALS | MATHEMATICS | modified q-Euler numbers with weight alpha and beta | HIGHER-ORDER | modified q-Genocchi numbers with weight alpha and beta

Modified q-Genocchi numbers with weight alpha and beta | Modified q-Euler numbers with weight alpha and beta | p-adic log gamma functions | POLYNOMIALS | INTEGRALS | MATHEMATICS | modified q-Euler numbers with weight alpha and beta | HIGHER-ORDER | modified q-Genocchi numbers with weight alpha and beta

Journal Article

Journal of Number Theory, ISSN 0022-314X, 2011, Volume 131, Issue 7, pp. 1240 - 1257

We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their...

Volkenborn integral | Barnes multiple zeta functions | p-Adic analysis | Multiple gamma functions | Diamond function | P-Adic analysis | MATHEMATICS | VALUES | EULER | Heterocyclic compounds | Universities and colleges

Volkenborn integral | Barnes multiple zeta functions | p-Adic analysis | Multiple gamma functions | Diamond function | P-Adic analysis | MATHEMATICS | VALUES | EULER | Heterocyclic compounds | Universities and colleges

Journal Article

Journal of Number Theory, ISSN 0022-314X, 04/2014, Volume 137, pp. 256 - 257

Journal Article

Finite Fields and their Applications, ISSN 1071-5797, 2015, Volume 33, pp. 230 - 231

We correct the statements of Lemma 3.2 and Lemma 3.3 in [1].

Characters of finite fields | Teichmüller character | Gauss sums | p-adic Gamma function

Characters of finite fields | Teichmüller character | Gauss sums | p-adic Gamma function

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 471, Issue 1-2, pp. 613 - 622

In 1997, Van Hamme conjectured 13 Ramanujan-type supercongruences labeled (A.2)–(M.2). Using some combinatorial identities discovered by Sigma, we extend (A.2)...

p-adic Gamma functions | Hypergeometric series | Supercongruences | MATHEMATICS | MATHEMATICS, APPLIED

p-adic Gamma functions | Hypergeometric series | Supercongruences | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 02/2019, Volume 15, Issue 1, pp. 67 - 84

In this paper, we primarily consider a generalization of the fermionic p -adic q -integral on ℤ p including the parameters α and β and investigate its some...

p -adic Euler constant | p -adic gamma function | Stirling numbers of the first kind | Mahler expansion | q -Euler polynomials | q -calculus | p -adic q -integral | q -Changhee polynomials | Stirling numbers of the second kind | Changhee polynomials | p -adic number | MATHEMATICS | p-adic q-integral | p-adic number | p-adic gamma function | q-Changhee polynomials | p-adic Euler constant | q-Euler polynomials | q-calculus

p -adic Euler constant | p -adic gamma function | Stirling numbers of the first kind | Mahler expansion | q -Euler polynomials | q -calculus | p -adic q -integral | q -Changhee polynomials | Stirling numbers of the second kind | Changhee polynomials | p -adic number | MATHEMATICS | p-adic q-integral | p-adic number | p-adic gamma function | q-Changhee polynomials | p-adic Euler constant | q-Euler polynomials | q-calculus

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 290, pp. 773 - 808

For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove...

p-adic Gamma functions | Hypergeometric series | Supercongruences | MATHEMATICS

p-adic Gamma functions | Hypergeometric series | Supercongruences | MATHEMATICS

Journal Article

Inventiones mathematicae, ISSN 1432-1297, 2019, Volume 217, Issue 3, pp. 985 - 1068

We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group...

22E50 | Mathematics, general | Mathematics | Primary 11F70 | Secondary 11F55 | 22E55 | 11F66 | GAMMA-FACTORS | CLASSICAL-GROUPS | THEOREM | RANKIN-SELBERG INTEGRALS | BESSEL MODELS | P-ADIC GROUPS | RESIDUAL SPECTRUM | MATHEMATICS | INDUCED REPRESENTATIONS | UNRAMIFIED PRINCIPAL SERIES | FUNCTORIALITY | Mathematical analysis | Tensors | Representations

22E50 | Mathematics, general | Mathematics | Primary 11F70 | Secondary 11F55 | 22E55 | 11F66 | GAMMA-FACTORS | CLASSICAL-GROUPS | THEOREM | RANKIN-SELBERG INTEGRALS | BESSEL MODELS | P-ADIC GROUPS | RESIDUAL SPECTRUM | MATHEMATICS | INDUCED REPRESENTATIONS | UNRAMIFIED PRINCIPAL SERIES | FUNCTORIALITY | Mathematical analysis | Tensors | Representations

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 12/2016, Volume 12, Issue 8, pp. 2125 - 2145

... of Gauss factorials that resemble binomial coefficients and are related to Morita's p -adic gamma function...

p -adic gamma function | congruences | Catalan numbers | Binomial coefficients | factorials | Jacobi sums | MATHEMATICS | p-adic gamma function | Heterocyclic compounds

p -adic gamma function | congruences | Catalan numbers | Binomial coefficients | factorials | Jacobi sums | MATHEMATICS | p-adic gamma function | Heterocyclic compounds

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 10/2016, Volume 94, Issue 2, pp. 208 - 216

... $q\not \equiv 1\,(\text{mod}\,d)$ in terms of McCarthy’s $p$ -adic hypergeometric function for any odd prime $d$ .

hypergeometric series | Teichmüller character | Dwork hypersurfaces | p-adic gamma function | and phrases characters of finite fields

hypergeometric series | Teichmüller character | Dwork hypersurfaces | p-adic gamma function | and phrases characters of finite fields

Journal Article

Annales mathématiques du Québec, ISSN 2195-4755, 10/2018, Volume 42, Issue 2, pp. 133 - 157

... $$\mathbb {F}_p$$ Fp . Salerno expresses the number of points over a finite field $$\mathbb {F}_p$$ Fp on the family $$Z_{\lambda }$$ Zλ in terms of quotients of p-adic gamma functions under the condition...

11S80 | Teichmüller character | Secondary 33C99 | 33E50 | Gaussian hypergeometric series | Mathematics | p -adic Gamma function | Primary 11G20 | Jacobi sums | Algebra | Gauss sums | Analysis | Character of finite fields | p -adic hypergeometric series | Mathematics, general | Algebraic curves | Number Theory | 11T24 | p-adic Gamma function | p-adic hypergeometric series

11S80 | Teichmüller character | Secondary 33C99 | 33E50 | Gaussian hypergeometric series | Mathematics | p -adic Gamma function | Primary 11G20 | Jacobi sums | Algebra | Gauss sums | Analysis | Character of finite fields | p -adic hypergeometric series | Mathematics, general | Algebraic curves | Number Theory | 11T24 | p-adic Gamma function | p-adic hypergeometric series

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2018, Volume 20, Issue 11, pp. 2813 - 2858

... some applications, such as the stability of Langlands-Shahidi gamma-factors and the local Langlands correspondence for classical groups.

Local Langlands correspondence | Globalization | Supercuspidal representations | Function fields | GAMMA-FACTORS | local Langlands correspondence | MATHEMATICS, APPLIED | function fields | CLASSICAL-GROUPS | TAMAGAWA NUMBERS | PARAMETERS | CONJECTURE | P-ADIC GROUPS | ALGEBRAIC-GROUPS | MATHEMATICS | DISCRETE-SERIES | REDUCTIVE GROUPS | supercuspidal representations

Local Langlands correspondence | Globalization | Supercuspidal representations | Function fields | GAMMA-FACTORS | local Langlands correspondence | MATHEMATICS, APPLIED | function fields | CLASSICAL-GROUPS | TAMAGAWA NUMBERS | PARAMETERS | CONJECTURE | P-ADIC GROUPS | ALGEBRAIC-GROUPS | MATHEMATICS | DISCRETE-SERIES | REDUCTIVE GROUPS | supercuspidal representations

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2010, Volume 145, Issue 2, pp. 109 - 122

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 03/2015, Volume 11, Issue 2, pp. 645 - 660

In [The trace of Frobenius of elliptic curves and the p-adic gamma function, Pacific J. Math. 261(1) (2013) 219–236...

trace of Frobenius | Character of finite fields | Teichmüller character | elliptic curves | Gaussian hypergeometric series | p-adic Gamma function | Teichmuller character | TRACE | MATHEMATICS | ELLIPTIC-CURVES | GAMMA-FUNCTION | FROBENIUS

trace of Frobenius | Character of finite fields | Teichmüller character | elliptic curves | Gaussian hypergeometric series | p-adic Gamma function | Teichmuller character | TRACE | MATHEMATICS | ELLIPTIC-CURVES | GAMMA-FUNCTION | FROBENIUS

Journal Article

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